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: \( 3.9173719233 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.677178763\) \(a_{4}=+0.000000000\) \(a_{5}=-0.786410329\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.643691896\) \(a_{8}=+0.000000000\) \(a_{9}=+1.812928604\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.187732071\) \(a_{12}=+0.000000000\) \(a_{13}=-1.450503854\) \(a_{14}=+0.000000000\) \(a_{15}=-1.318950702\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.992395993\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.756765141\) \(a_{22}=+0.000000000\) \(a_{23}=-0.302298720\) \(a_{24}=+0.000000000\) \(a_{25}=-0.381558795\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.363426590\) \(a_{28}=+0.000000000\) \(a_{29}=-0.818656304\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.305572348\) \(a_{32}=+0.000000000\) \(a_{33}=+0.314860242\) \(a_{34}=+0.000000000\) \(a_{35}=+1.292616284\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.377128975\) \(a_{38}=+0.000000000\) \(a_{39}=-2.432754260\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.385581672\) \(a_{42}=+0.000000000\) \(a_{43}=-1.264923993\) \(a_{44}=+0.000000000\) \(a_{45}=-1.425705779\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.902605886\) \(a_{48}=+0.000000000\) \(a_{49}=+1.701723049\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.406775600\) \(a_{52}=+0.000000000\) \(a_{53}=-0.803705540\) \(a_{54}=+0.000000000\) \(a_{55}=-0.147634439\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.664425485\) \(a_{58}=+0.000000000\) \(a_{59}=+1.545344029\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.264900469\) \(a_{62}=+0.000000000\) \(a_{63}=-2.979896054\) \(a_{64}=+0.000000000\) \(a_{65}=+1.140691212\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.378457538\) \(a_{68}=+0.000000000\) \(a_{69}=-0.507008994\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.139227775\) \(a_{72}=+0.000000000\) \(a_{73}=+1.600978097\) \(a_{74}=+0.000000000\) \(a_{75}=-0.639942308\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.308573683\) \(a_{78}=+0.000000000\) \(a_{79}=+0.576758303\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.473781518\) \(a_{82}=+0.000000000\) \(a_{83}=-1.171319874\) \(a_{84}=+0.000000000\) \(a_{85}=-0.190732521\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.373032968\) \(a_{88}=+0.000000000\) \(a_{89}=+0.068303598\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.384181430\) \(a_{92}=+0.000000000\) \(a_{93}=+2.189678215\) \(a_{94}=+0.000000000\) \(a_{95}=+0.780430459\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.655443739\) \(a_{98}=+0.000000000\) \(a_{99}=+0.340344841\) \(a_{100}=+0.000000000\)

Showing 100 of 630 available coefficients

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