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: \( 3.2322374747 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.313196480\) \(a_{4}=+0.000000000\) \(a_{5}=-1.200752677\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.903162043\) \(a_{8}=+0.000000000\) \(a_{9}=+0.724484995\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.809562247\) \(a_{12}=+0.000000000\) \(a_{13}=+0.561714358\) \(a_{14}=+0.000000000\) \(a_{15}=+1.576824189\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.770891159\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.186029215\) \(a_{22}=+0.000000000\) \(a_{23}=-0.013440406\) \(a_{24}=+0.000000000\) \(a_{25}=+0.441806992\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.361805335\) \(a_{28}=+0.000000000\) \(a_{29}=-1.630093780\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.209866478\) \(a_{32}=+0.000000000\) \(a_{33}=-1.063114293\) \(a_{34}=+0.000000000\) \(a_{35}=+1.084474241\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.177783064\) \(a_{38}=+0.000000000\) \(a_{39}=-0.737641317\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.943108077\) \(a_{42}=+0.000000000\) \(a_{43}=+0.981978664\) \(a_{44}=+0.000000000\) \(a_{45}=-0.869927297\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.772830729\) \(a_{48}=+0.000000000\) \(a_{49}=-0.184298324\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.318496929\) \(a_{52}=+0.000000000\) \(a_{53}=+1.673250226\) \(a_{54}=+0.000000000\) \(a_{55}=-0.972084035\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.012331556\) \(a_{58}=+0.000000000\) \(a_{59}=+1.953877963\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.699052374\) \(a_{62}=+0.000000000\) \(a_{63}=-0.654327348\) \(a_{64}=+0.000000000\) \(a_{65}=-0.674480019\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.678124737\) \(a_{68}=+0.000000000\) \(a_{69}=+0.017649894\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.737304644\) \(a_{72}=+0.000000000\) \(a_{73}=-0.352997463\) \(a_{74}=+0.000000000\) \(a_{75}=-0.580179386\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.731165893\) \(a_{78}=+0.000000000\) \(a_{79}=-0.568953790\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.199606487\) \(a_{82}=+0.000000000\) \(a_{83}=+1.873980952\) \(a_{84}=+0.000000000\) \(a_{85}=+0.291225301\)
\(a_{86}=+0.000000000\) \(a_{87}=+2.140633414\) \(a_{88}=+0.000000000\) \(a_{89}=+0.052899017\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.507319087\) \(a_{92}=+0.000000000\) \(a_{93}=-1.588792400\) \(a_{94}=+0.000000000\) \(a_{95}=+0.925649623\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.103962196\) \(a_{98}=+0.000000000\) \(a_{99}=+0.586515700\) \(a_{100}=+0.000000000\)

Showing 100 of 556 available coefficients

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