Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.75813319502 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.199772466\) \(a_{3}=+0.577350269\) \(a_{4}=+0.439453970\) \(a_{5}=+1.365676578\)
\(a_{6}=-0.692688958\) \(a_{7}=+0.135013131\) \(a_{8}=+0.672527659\) \(a_{9}=+0.333333517\) \(a_{10}=-1.638502165\)
\(a_{11}=+1.043553676\) \(a_{12}=+0.253687309\) \(a_{13}=-0.261063821\) \(a_{14}=-0.161985030\) \(a_{15}=+0.788473740\)
\(a_{16}=-1.246334178\) \(a_{17}=+0.390209743\) \(a_{18}=-0.399924155\) \(a_{19}=+0.813928643\) \(a_{20}=+0.600151994\)
\(a_{21}=+0.077949864\) \(a_{22}=-1.252020217\) \(a_{23}=-0.781389862\) \(a_{24}=+0.388284044\) \(a_{25}=+0.865072515\)
\(a_{26}=+0.313429557\) \(a_{27}=+0.192450090\) \(a_{28}=+0.059332054\) \(a_{29}=-0.334609658\) \(a_{30}=-0.945989083\)
\(a_{31}=-0.494111781\) \(a_{32}=+0.822789738\) \(a_{33}=+0.602492747\) \(a_{34}=-0.468162905\) \(a_{35}=+0.184384262\)
\(a_{36}=+0.146484657\) \(a_{37}=+0.658401027\) \(a_{38}=-0.976529175\) \(a_{39}=-0.150827465\) \(a_{40}=+0.918455319\)
\(a_{41}=-0.568561752\) \(a_{42}=-0.093522102\) \(a_{43}=-1.521575114\) \(a_{44}=+0.458591334\) \(a_{45}=+0.455225531\)
\(a_{46}=+0.937490037\) \(a_{47}=+1.859478649\) \(a_{48}=-0.719571372\) \(a_{49}=-0.981771443\) \(a_{50}=-1.037890167\)
\(a_{51}=+0.225287658\) \(a_{52}=-0.114803342\) \(a_{53}=-0.737100400\) \(a_{54}=-0.230896220\) \(a_{55}=+1.425149131\)
\(a_{56}=+0.090799806\) \(a_{57}=+0.469921926\) \(a_{58}=+0.401455694\) \(a_{59}=-0.210144060\) \(a_{60}=+0.346497918\)
\(a_{61}=-1.840964582\) \(a_{62}=+0.592821706\) \(a_{63}=+0.045004372\) \(a_{64}=+0.259173710\) \(a_{65}=-0.356770479\)
\(a_{66}=-0.722854213\) \(a_{67}=+0.669609405\) \(a_{68}=+0.171479219\) \(a_{69}=-0.451135626\) \(a_{70}=-0.221219148\)
\(a_{71}=+1.186764160\) \(a_{72}=+0.224175861\) \(a_{73}=+0.061058389\) \(a_{74}=-0.789931353\) \(a_{75}=+0.499449859\)
\(a_{76}=+0.357684068\) \(a_{77}=+0.140892603\) \(a_{78}=+0.180958768\) \(a_{79}=-1.268384900\) \(a_{80}=-1.702089490\)
\(a_{81}=+0.111110744\) \(a_{82}=+0.682144671\) \(a_{83}=+0.161327225\) \(a_{84}=+0.034255785\) \(a_{85}=+0.532899632\)
\(a_{86}=+1.825542880\) \(a_{87}=-0.193186493\) \(a_{88}=+0.701816944\) \(a_{89}=-0.953117311\) \(a_{90}=-0.546169990\)
\(a_{91}=-0.035273173\) \(a_{92}=-0.343381402\) \(a_{93}=-0.285270046\) \(a_{94}=-2.230953760\) \(a_{95}=+1.111553178\)
\(a_{96}=+0.475035907\) \(a_{97}=+0.023378246\) \(a_{98}=+1.177913980\) \(a_{99}=+0.347831547\) \(a_{100}=+0.380130726\)

Showing 100 of 5000 available coefficients

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