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: \( 5.89053901655 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.204951319\) \(a_{4}=+0.000000000\) \(a_{5}=-0.416777903\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.174517879\) \(a_{8}=+0.000000000\) \(a_{9}=+0.451907682\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.895333902\) \(a_{12}=+0.000000000\) \(a_{13}=-0.539748405\) \(a_{14}=+0.000000000\) \(a_{15}=-0.502197084\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-1.090928698\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.415236868\) \(a_{22}=+0.000000000\) \(a_{23}=+0.600073453\) \(a_{24}=+0.000000000\) \(a_{25}=-0.826296180\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.660424562\) \(a_{28}=+0.000000000\) \(a_{29}=+0.486046506\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.892586790\) \(a_{32}=+0.000000000\) \(a_{33}=-2.283785086\) \(a_{34}=+0.000000000\) \(a_{35}=-0.489513098\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.655915706\) \(a_{38}=+0.000000000\) \(a_{39}=-0.650370553\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.748037691\) \(a_{42}=+0.000000000\) \(a_{43}=-1.710269714\) \(a_{44}=+0.000000000\) \(a_{45}=-0.188345136\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.521469939\) \(a_{48}=+0.000000000\) \(a_{49}=+0.379492247\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.292243621\) \(a_{52}=+0.000000000\) \(a_{53}=-1.214677140\) \(a_{54}=+0.000000000\) \(a_{55}=+0.789933289\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.314515974\) \(a_{58}=+0.000000000\) \(a_{59}=+0.031682154\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.429686061\) \(a_{62}=+0.000000000\) \(a_{63}=+0.530773652\) \(a_{64}=+0.000000000\) \(a_{65}=+0.224955208\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.371400334\) \(a_{68}=+0.000000000\) \(a_{69}=+0.723059299\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.133420926\) \(a_{72}=+0.000000000\) \(a_{73}=-1.109473039\) \(a_{74}=+0.000000000\) \(a_{75}=-0.995646672\)
\(a_{76}=+0.000000000\) \(a_{77}=-2.226103554\) \(a_{78}=+0.000000000\) \(a_{79}=+1.415634797\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.247687129\) \(a_{82}=+0.000000000\) \(a_{83}=-1.724265592\) \(a_{84}=+0.000000000\) \(a_{85}=-0.101083489\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.585662378\) \(a_{88}=+0.000000000\) \(a_{89}=-1.300671833\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.633944152\) \(a_{92}=+0.000000000\) \(a_{93}=+1.075523630\) \(a_{94}=+0.000000000\) \(a_{95}=+0.454674974\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.180330661\) \(a_{98}=+0.000000000\) \(a_{99}=-0.856515950\) \(a_{100}=+0.000000000\)

Showing 100 of 700 available coefficients

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