Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.98548264489 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.582888434\) \(a_{4}=+0.000000000\) \(a_{5}=+0.674950627\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.037381450\) \(a_{8}=+0.000000000\) \(a_{9}=+1.505535793\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.699830385\) \(a_{12}=+0.000000000\) \(a_{13}=-0.719542716\) \(a_{14}=+0.000000000\) \(a_{15}=+1.068371541\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+1.632102924\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.059170665\) \(a_{22}=+0.000000000\) \(a_{23}=+0.495055266\) \(a_{24}=+0.000000000\) \(a_{25}=-0.544441651\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.800206759\) \(a_{28}=+0.000000000\) \(a_{29}=+1.268723618\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.707610753\) \(a_{32}=+0.000000000\) \(a_{33}=-2.690641855\) \(a_{34}=+0.000000000\) \(a_{35}=-0.025230633\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.566426772\) \(a_{38}=+0.000000000\) \(a_{39}=-1.138955842\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.631421159\) \(a_{42}=+0.000000000\) \(a_{43}=-0.232152575\) \(a_{44}=+0.000000000\) \(a_{45}=+1.016162327\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.635553215\) \(a_{48}=+0.000000000\) \(a_{49}=-0.998602627\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.383906836\) \(a_{52}=+0.000000000\) \(a_{53}=+0.790659529\) \(a_{54}=+0.000000000\) \(a_{55}=-1.147301584\)
\(a_{56}=+0.000000000\) \(a_{57}=+2.583436841\) \(a_{58}=+0.000000000\) \(a_{59}=-1.534866063\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.370386155\) \(a_{62}=+0.000000000\) \(a_{63}=-0.056279111\) \(a_{64}=+0.000000000\) \(a_{65}=-0.485655807\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.014935420\) \(a_{68}=+0.000000000\) \(a_{69}=+0.783617254\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.092156310\) \(a_{72}=+0.000000000\) \(a_{73}=-0.746949329\) \(a_{74}=+0.000000000\) \(a_{75}=-0.861790392\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.063542124\) \(a_{78}=+0.000000000\) \(a_{79}=-0.173552148\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.238897769\) \(a_{82}=+0.000000000\) \(a_{83}=+0.825383620\) \(a_{84}=+0.000000000\) \(a_{85}=+0.163699572\)
\(a_{86}=+0.000000000\) \(a_{87}=+2.008247941\) \(a_{88}=+0.000000000\) \(a_{89}=+0.380183489\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.026897550\) \(a_{92}=+0.000000000\) \(a_{93}=+1.120068876\) \(a_{94}=+0.000000000\) \(a_{95}=+1.101588892\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.884007788\) \(a_{98}=+0.000000000\) \(a_{99}=-2.559155486\) \(a_{100}=+0.000000000\)

Showing 100 of 742 available coefficients

Rows: Cols: