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: \( 5.70114750514 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.594323491\) \(a_{4}=+0.000000000\) \(a_{5}=+0.472738324\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.965952407\) \(a_{8}=+0.000000000\) \(a_{9}=+1.541867395\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.615726684\) \(a_{12}=+0.000000000\) \(a_{13}=+0.300942703\) \(a_{14}=+0.000000000\) \(a_{15}=+0.753697815\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.197847081\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.540040614\) \(a_{22}=+0.000000000\) \(a_{23}=-0.113112617\) \(a_{24}=+0.000000000\) \(a_{25}=-0.776518477\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.863911916\) \(a_{28}=+0.000000000\) \(a_{29}=-1.297966604\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.935425051\) \(a_{32}=+0.000000000\) \(a_{33}=+0.981667517\) \(a_{34}=+0.000000000\) \(a_{35}=+0.456642722\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.281401164\) \(a_{38}=+0.000000000\) \(a_{39}=+0.479800021\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.743453938\) \(a_{42}=+0.000000000\) \(a_{43}=-0.071181075\) \(a_{44}=+0.000000000\) \(a_{45}=+0.728899808\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.551224318\) \(a_{48}=+0.000000000\) \(a_{49}=-0.066935946\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.386680244\) \(a_{52}=+0.000000000\) \(a_{53}=+1.644117860\) \(a_{54}=+0.000000000\) \(a_{55}=+0.291077601\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.315432249\) \(a_{58}=+0.000000000\) \(a_{59}=-0.896458535\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.307496750\) \(a_{62}=+0.000000000\) \(a_{63}=+1.489370522\) \(a_{64}=+0.000000000\) \(a_{65}=+0.142267149\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.060748639\) \(a_{68}=+0.000000000\) \(a_{69}=-0.180338102\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.504078765\) \(a_{72}=+0.000000000\) \(a_{73}=-0.164598484\) \(a_{74}=+0.000000000\) \(a_{75}=-1.238021650\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.594762673\) \(a_{78}=+0.000000000\) \(a_{79}=-1.363285594\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.164512332\) \(a_{82}=+0.000000000\) \(a_{83}=-1.557975162\) \(a_{84}=+0.000000000\) \(a_{85}=+0.114655885\)
\(a_{86}=+0.000000000\) \(a_{87}=-2.069378648\) \(a_{88}=+0.000000000\) \(a_{89}=+0.846228554\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.290696329\) \(a_{92}=+0.000000000\) \(a_{93}=+1.491370133\) \(a_{94}=+0.000000000\) \(a_{95}=+0.093529897\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.233124659\) \(a_{98}=+0.000000000\) \(a_{99}=+0.949368898\) \(a_{100}=+0.000000000\)

Showing 100 of 672 available coefficients

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