Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.75060456267 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.130210019\) \(a_{3}=-0.739993180\) \(a_{4}=-0.983045351\) \(a_{5}=-0.085985160\)
\(a_{6}=-0.096354526\) \(a_{7}=+0.615790732\) \(a_{8}=-0.258212372\) \(a_{9}=-0.452410094\) \(a_{10}=-0.011196129\)
\(a_{11}=-1.249003007\) \(a_{12}=+0.727446855\) \(a_{13}=-0.277350098\) \(a_{14}=+0.080182123\) \(a_{15}=+0.063628432\)
\(a_{16}=+0.949423513\) \(a_{17}=+0.789509821\) \(a_{18}=-0.058908327\) \(a_{19}=-1.012046458\) \(a_{20}=+0.084527312\)
\(a_{21}=-0.455680942\) \(a_{22}=-0.162632705\) \(a_{23}=+0.176558977\) \(a_{24}=+0.191075394\) \(a_{25}=-0.992606552\)
\(a_{26}=-0.036113761\) \(a_{27}=+1.074773564\) \(a_{28}=-0.605350216\) \(a_{29}=-0.564953717\) \(a_{30}=+0.008285059\)
\(a_{31}=+0.788042718\) \(a_{32}=+0.381836825\) \(a_{33}=+0.924253707\) \(a_{34}=+0.102802088\) \(a_{35}=-0.052948865\)
\(a_{36}=+0.444739639\) \(a_{37}=-0.705745985\) \(a_{38}=-0.131778588\) \(a_{39}=+0.205237181\) \(a_{40}=+0.022202432\)
\(a_{41}=-1.838075688\) \(a_{42}=-0.059334224\) \(a_{43}=-1.287250029\) \(a_{44}=+1.227826600\) \(a_{45}=+0.038900554\)
\(a_{46}=+0.022989748\) \(a_{47}=+1.936666617\) \(a_{48}=-0.702566925\) \(a_{49}=-0.620801775\) \(a_{50}=-0.129247318\)
\(a_{51}=-0.584231883\) \(a_{52}=+0.272647725\) \(a_{53}=+0.590914114\) \(a_{54}=+0.139946286\) \(a_{55}=+0.107395724\)
\(a_{56}=-0.159004785\) \(a_{57}=+0.748907477\) \(a_{58}=-0.073562634\) \(a_{59}=+0.943319927\) \(a_{60}=-0.062549635\)
\(a_{61}=+0.248986868\) \(a_{62}=+0.102611057\) \(a_{63}=-0.278589943\) \(a_{64}=-0.899704533\) \(a_{65}=+0.023847993\)
\(a_{66}=+0.120347092\) \(a_{67}=-1.270576442\) \(a_{68}=-0.776123959\) \(a_{69}=-0.130652439\) \(a_{70}=-0.006894473\)
\(a_{71}=+0.300709979\) \(a_{72}=+0.116817883\) \(a_{73}=-0.895003470\) \(a_{74}=-0.091895198\) \(a_{75}=+0.734522079\)
\(a_{76}=+0.994887566\) \(a_{77}=-0.769124476\) \(a_{78}=+0.026723937\) \(a_{79}=+1.798895748\) \(a_{80}=-0.081636333\)
\(a_{81}=-0.342915013\) \(a_{82}=-0.239335869\) \(a_{83}=+0.010034698\) \(a_{84}=+0.447955031\) \(a_{85}=-0.067886129\)
\(a_{86}=-0.167612850\) \(a_{87}=+0.418061897\) \(a_{88}=+0.322508029\) \(a_{89}=+0.466455649\) \(a_{90}=+0.005065242\)
\(a_{91}=-0.170789620\) \(a_{92}=-0.173565481\) \(a_{93}=-0.583146237\) \(a_{94}=+0.252173396\) \(a_{95}=+0.087020977\)
\(a_{96}=-0.282556647\) \(a_{97}=-1.647984655\) \(a_{98}=-0.080834611\) \(a_{99}=+0.565061568\) \(a_{100}=+0.975777257\)

Showing 100 of 546 available coefficients

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