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: \( 4.65558565106 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.948924379\) \(a_{4}=+0.000000000\) \(a_{5}=-1.446096582\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.332740550\) \(a_{8}=+0.000000000\) \(a_{9}=+2.798306234\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.257476825\) \(a_{12}=+0.000000000\) \(a_{13}=-0.143290449\) \(a_{14}=+0.000000000\) \(a_{15}=+2.818332882\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.714176613\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.597410548\) \(a_{22}=+0.000000000\) \(a_{23}=+1.537151636\) \(a_{24}=+0.000000000\) \(a_{25}=+1.091195324\)
\(a_{26}=+0.000000000\) \(a_{27}=-3.504762859\) \(a_{28}=+0.000000000\) \(a_{29}=+1.000488352\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.999507002\) \(a_{32}=+0.000000000\) \(a_{33}=+0.501802860\) \(a_{34}=+0.000000000\) \(a_{35}=-1.927271553\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.547582739\) \(a_{38}=+0.000000000\) \(a_{39}=+0.279262249\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.038340034\) \(a_{42}=+0.000000000\) \(a_{43}=-0.197481831\) \(a_{44}=+0.000000000\) \(a_{45}=-4.046621079\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.844207888\) \(a_{48}=+0.000000000\) \(a_{49}=+0.776197373\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.472683592\) \(a_{52}=+0.000000000\) \(a_{53}=+0.621962771\) \(a_{54}=+0.000000000\) \(a_{55}=+0.372336356\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.391876212\) \(a_{58}=+0.000000000\) \(a_{59}=-0.938206328\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.160286901\) \(a_{62}=+0.000000000\) \(a_{63}=+3.729416188\) \(a_{64}=+0.000000000\) \(a_{65}=+0.207211828\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.185123075\) \(a_{68}=+0.000000000\) \(a_{69}=-2.995792297\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.519832018\) \(a_{72}=+0.000000000\) \(a_{73}=+0.342644551\) \(a_{74}=+0.000000000\) \(a_{75}=-2.126657168\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.343149805\) \(a_{78}=+0.000000000\) \(a_{79}=-0.610601505\) \(a_{80}=+0.000000000\)
\(a_{81}=+4.032211543\) \(a_{82}=+0.000000000\) \(a_{83}=-0.820564331\) \(a_{84}=+0.000000000\) \(a_{85}=+0.350729938\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.949876140\) \(a_{88}=+0.000000000\) \(a_{89}=-0.083870413\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.190968992\) \(a_{92}=+0.000000000\) \(a_{93}=-1.947963563\) \(a_{94}=+0.000000000\) \(a_{95}=+1.032768359\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.638885844\) \(a_{98}=+0.000000000\) \(a_{99}=-0.720499003\) \(a_{100}=+0.000000000\)

Showing 100 of 618 available coefficients

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