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: \( 0.901444248535 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.573287267\) \(a_{4}=+0.000000000\) \(a_{5}=-1.484091239\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.142056482\) \(a_{8}=+0.000000000\) \(a_{9}=+1.475232824\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.115606322\) \(a_{12}=+0.000000000\) \(a_{13}=-0.899233293\) \(a_{14}=+0.000000000\) \(a_{15}=+2.334901850\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.212781736\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.223495654\) \(a_{22}=+0.000000000\) \(a_{23}=-1.956480370\) \(a_{24}=+0.000000000\) \(a_{25}=+1.202526807\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.747677751\) \(a_{28}=+0.000000000\) \(a_{29}=+0.248601119\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.564217466\) \(a_{32}=+0.000000000\) \(a_{33}=+0.181881954\) \(a_{34}=+0.000000000\) \(a_{35}=-0.210824780\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.464935527\) \(a_{38}=+0.000000000\) \(a_{39}=+1.414752289\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.082048574\) \(a_{42}=+0.000000000\) \(a_{43}=+0.270028098\) \(a_{44}=+0.000000000\) \(a_{45}=-2.189380111\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.329101381\) \(a_{48}=+0.000000000\) \(a_{49}=-0.979819956\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.381578211\) \(a_{52}=+0.000000000\) \(a_{53}=+0.731671975\) \(a_{54}=+0.000000000\) \(a_{55}=+0.171570329\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.334766796\) \(a_{58}=+0.000000000\) \(a_{59}=-0.063961661\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.343383809\) \(a_{62}=+0.000000000\) \(a_{63}=+0.209566385\) \(a_{64}=+0.000000000\) \(a_{65}=+1.334544252\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.528051697\) \(a_{68}=+0.000000000\) \(a_{69}=+3.078105654\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.540234159\) \(a_{72}=+0.000000000\) \(a_{73}=-0.601172751\) \(a_{74}=+0.000000000\) \(a_{75}=-1.891920114\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.016422627\) \(a_{78}=+0.000000000\) \(a_{79}=-0.899225913\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.298920939\) \(a_{82}=+0.000000000\) \(a_{83}=-1.531885618\) \(a_{84}=+0.000000000\) \(a_{85}=-0.359944996\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.391120974\) \(a_{88}=+0.000000000\) \(a_{89}=-0.864172372\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.127741918\) \(a_{92}=+0.000000000\) \(a_{93}=+0.887676155\) \(a_{94}=+0.000000000\) \(a_{95}=-0.315787511\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.874402871\) \(a_{98}=+0.000000000\) \(a_{99}=-0.170546240\) \(a_{100}=+0.000000000\)

Showing 100 of 612 available coefficients

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