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: \( 4.80145189189 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.613543675\) \(a_{4}=+0.000000000\) \(a_{5}=-1.106261636\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.129890340\) \(a_{8}=+0.000000000\) \(a_{9}=+1.603523191\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.660131597\) \(a_{12}=+0.000000000\) \(a_{13}=+0.125223245\) \(a_{14}=+0.000000000\) \(a_{15}=-1.785001466\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.442702764\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.209583738\) \(a_{22}=+0.000000000\) \(a_{23}=-1.461668799\) \(a_{24}=+0.000000000\) \(a_{25}=+0.223814808\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.973811028\) \(a_{28}=+0.000000000\) \(a_{29}=-0.716191182\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.857594507\) \(a_{32}=+0.000000000\) \(a_{33}=-2.678694838\) \(a_{34}=+0.000000000\) \(a_{35}=-0.143692701\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.202757660\) \(a_{38}=+0.000000000\) \(a_{39}=+0.202053175\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.334787935\) \(a_{42}=+0.000000000\) \(a_{43}=+1.687213461\) \(a_{44}=+0.000000000\) \(a_{45}=-1.773916189\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.687329985\) \(a_{48}=+0.000000000\) \(a_{49}=-0.983128499\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.391341824\) \(a_{52}=+0.000000000\) \(a_{53}=-1.735242879\) \(a_{54}=+0.000000000\) \(a_{55}=+1.836539897\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.714320245\) \(a_{58}=+0.000000000\) \(a_{59}=-0.556636123\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.156851395\) \(a_{62}=+0.000000000\) \(a_{63}=+0.208282173\) \(a_{64}=+0.000000000\) \(a_{65}=-0.138529672\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.517666760\) \(a_{68}=+0.000000000\) \(a_{69}=-2.358466446\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.936091702\) \(a_{72}=+0.000000000\) \(a_{73}=+1.673254917\) \(a_{74}=+0.000000000\) \(a_{75}=+0.361134967\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.215635058\) \(a_{78}=+0.000000000\) \(a_{79}=+0.635908091\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.032236566\) \(a_{82}=+0.000000000\) \(a_{83}=+0.918664571\) \(a_{84}=+0.000000000\) \(a_{85}=+0.268307857\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.155605752\) \(a_{88}=+0.000000000\) \(a_{89}=-0.114190219\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.016265290\) \(a_{92}=+0.000000000\) \(a_{93}=-1.383766192\) \(a_{94}=+0.000000000\) \(a_{95}=-0.489745084\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.607019892\) \(a_{98}=+0.000000000\) \(a_{99}=-2.662059517\) \(a_{100}=+0.000000000\)

Showing 100 of 640 available coefficients

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