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: \( 3.96874716436 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.063528735\) \(a_{4}=+0.000000000\) \(a_{5}=-0.305086000\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.572530741\) \(a_{8}=+0.000000000\) \(a_{9}=-0.995964100\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.092304593\) \(a_{12}=+0.000000000\) \(a_{13}=-1.640214943\) \(a_{14}=+0.000000000\) \(a_{15}=-0.019381728\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.867197362\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.099900889\) \(a_{22}=+0.000000000\) \(a_{23}=-1.323434774\) \(a_{24}=+0.000000000\) \(a_{25}=-0.906922533\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.126801075\) \(a_{28}=+0.000000000\) \(a_{29}=-1.584874108\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.106105960\) \(a_{32}=+0.000000000\) \(a_{33}=+0.005863994\) \(a_{34}=+0.000000000\) \(a_{35}=-0.479757114\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.730038874\) \(a_{38}=+0.000000000\) \(a_{39}=-0.104200781\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.484504137\) \(a_{42}=+0.000000000\) \(a_{43}=-1.802157058\) \(a_{44}=+0.000000000\) \(a_{45}=+0.303854704\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.829850797\) \(a_{48}=+0.000000000\) \(a_{49}=+1.472852930\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.015407981\) \(a_{52}=+0.000000000\) \(a_{53}=-0.197336102\) \(a_{54}=+0.000000000\) \(a_{55}=-0.028160839\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.055091951\) \(a_{58}=+0.000000000\) \(a_{59}=-0.281468905\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.248615626\) \(a_{62}=+0.000000000\) \(a_{63}=-1.566184164\) \(a_{64}=+0.000000000\) \(a_{65}=+0.500406616\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.006617157\) \(a_{68}=+0.000000000\) \(a_{69}=-0.084076137\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.173519811\) \(a_{72}=+0.000000000\) \(a_{73}=-0.487039177\) \(a_{74}=+0.000000000\) \(a_{75}=-0.057615641\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.145151810\) \(a_{78}=+0.000000000\) \(a_{79}=-1.525383722\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.987908588\) \(a_{82}=+0.000000000\) \(a_{83}=-0.841323420\) \(a_{84}=+0.000000000\) \(a_{85}=+0.073994224\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.100685047\) \(a_{88}=+0.000000000\) \(a_{89}=+0.297042948\) \(a_{90}=+0.000000000\)
\(a_{91}=-2.579288420\) \(a_{92}=+0.000000000\) \(a_{93}=+0.070269513\) \(a_{94}=+0.000000000\) \(a_{95}=-0.264569775\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.721242091\) \(a_{98}=+0.000000000\) \(a_{99}=-0.091932061\) \(a_{100}=+0.000000000\)

Showing 100 of 682 available coefficients

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