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: \( 4.18291899531 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.053940980\) \(a_{4}=+0.000000000\) \(a_{5}=-1.755927563\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.829554083\) \(a_{8}=+0.000000000\) \(a_{9}=-0.997090371\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.580070404\) \(a_{12}=+0.000000000\) \(a_{13}=+1.338783256\) \(a_{14}=+0.000000000\) \(a_{15}=-0.094716453\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.476574988\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.044746960\) \(a_{22}=+0.000000000\) \(a_{23}=+0.210896498\) \(a_{24}=+0.000000000\) \(a_{25}=+2.083281606\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.107725011\) \(a_{28}=+0.000000000\) \(a_{29}=+0.304513659\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.167502798\) \(a_{32}=+0.000000000\) \(a_{33}=+0.031289566\) \(a_{34}=+0.000000000\) \(a_{35}=+1.456636879\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.535257394\) \(a_{38}=+0.000000000\) \(a_{39}=+0.072215281\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.808305988\) \(a_{42}=+0.000000000\) \(a_{43}=-1.219931603\) \(a_{44}=+0.000000000\) \(a_{45}=+1.750818465\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.226592162\) \(a_{48}=+0.000000000\) \(a_{49}=-0.311840024\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.013082609\) \(a_{52}=+0.000000000\) \(a_{53}=+0.026029137\) \(a_{54}=+0.000000000\) \(a_{55}=-1.018561612\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.025706922\) \(a_{58}=+0.000000000\) \(a_{59}=-1.552982519\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.012262945\) \(a_{62}=+0.000000000\) \(a_{63}=+0.827140388\) \(a_{64}=+0.000000000\) \(a_{65}=-2.350806419\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.043230151\) \(a_{68}=+0.000000000\) \(a_{69}=+0.011375964\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.750653511\) \(a_{72}=+0.000000000\) \(a_{73}=-0.930063893\) \(a_{74}=+0.000000000\) \(a_{75}=+0.112374252\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.481199772\) \(a_{78}=+0.000000000\) \(a_{79}=+1.426009524\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.991279578\) \(a_{82}=+0.000000000\) \(a_{83}=+1.102043551\) \(a_{84}=+0.000000000\) \(a_{85}=-0.425874989\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.016425765\) \(a_{88}=+0.000000000\) \(a_{89}=-1.811068497\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.110593116\) \(a_{92}=+0.000000000\) \(a_{93}=+0.009035265\) \(a_{94}=+0.000000000\) \(a_{95}=+0.836831157\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.487605437\) \(a_{98}=+0.000000000\) \(a_{99}=-0.578382614\) \(a_{100}=+0.000000000\)

Showing 100 of 562 available coefficients

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