Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 36.8563494959 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.536575933\) \(a_{3}=+0.741765903\) \(a_{4}=-0.712086268\) \(a_{5}=+0.168588877\)
\(a_{6}=+0.398013732\) \(a_{7}=+0.311202353\) \(a_{8}=-0.918664287\) \(a_{9}=-0.449783345\) \(a_{10}=+0.090460734\)
\(a_{11}=+1.571827196\) \(a_{12}=-0.528201314\) \(a_{13}=+0.189718540\) \(a_{14}=+0.166983693\) \(a_{15}=+0.125053481\)
\(a_{16}=+0.219153120\) \(a_{17}=+1.549838899\) \(a_{18}=-0.241342922\) \(a_{19}=-0.423761195\) \(a_{20}=-0.120049824\)
\(a_{21}=+0.230839295\) \(a_{22}=+0.843404645\) \(a_{23}=+0.575947348\) \(a_{24}=-0.681433845\) \(a_{25}=-0.971577791\)
\(a_{26}=+0.101798403\) \(a_{27}=-1.075399852\) \(a_{28}=-0.221602922\) \(a_{29}=+1.775341942\) \(a_{30}=+0.067100688\)
\(a_{31}=+1.020096231\) \(a_{32}=+1.036256577\) \(a_{33}=+1.165927820\) \(a_{34}=+0.831606254\) \(a_{35}=+0.052465255\)
\(a_{36}=+0.320284543\) \(a_{37}=+1.160590087\) \(a_{38}=-0.227380082\) \(a_{39}=+0.140726744\) \(a_{40}=-0.154876580\)
\(a_{41}=+0.208127225\) \(a_{42}=+0.123862810\) \(a_{43}=+0.819257979\) \(a_{44}=-1.119276562\) \(a_{45}=-0.075828469\)
\(a_{46}=+0.309039486\) \(a_{47}=+0.592595972\) \(a_{48}=+0.162560312\) \(a_{49}=-0.903153095\) \(a_{50}=-0.521325260\)
\(a_{51}=+1.149617651\) \(a_{52}=-0.135095967\) \(a_{53}=+0.190466229\) \(a_{54}=-0.577033680\) \(a_{55}=+0.264992582\)
\(a_{56}=-0.285890488\) \(a_{57}=-0.314331637\) \(a_{58}=+0.952605760\) \(a_{59}=+0.033865922\) \(a_{60}=-0.089048866\)
\(a_{61}=-1.014355919\) \(a_{62}=+0.547359088\) \(a_{63}=-0.139973635\) \(a_{64}=+0.336877217\) \(a_{65}=+0.031984437\)
\(a_{66}=+0.625608817\) \(a_{67}=-0.505310808\) \(a_{68}=-1.103618997\) \(a_{69}=+0.427218105\) \(a_{70}=+0.028151593\)
\(a_{71}=+1.095019643\) \(a_{72}=+0.413199896\) \(a_{73}=-1.635990634\) \(a_{74}=+0.622744709\) \(a_{75}=-0.720683278\)
\(a_{76}=+0.301754558\) \(a_{77}=+0.489156322\) \(a_{78}=+0.075510584\) \(a_{79}=+0.026822262\) \(a_{80}=+0.036946778\)
\(a_{81}=-0.347911598\) \(a_{82}=+0.111676060\) \(a_{83}=-0.450847595\) \(a_{84}=-0.164377492\) \(a_{85}=+0.261285599\)
\(a_{86}=+0.439594115\) \(a_{87}=+1.316888119\) \(a_{88}=-1.443981511\) \(a_{89}=-0.314382749\) \(a_{90}=-0.040687731\)
\(a_{91}=+0.059040856\) \(a_{92}=-0.410124197\) \(a_{93}=+0.756672602\) \(a_{94}=+0.317972737\) \(a_{95}=-0.071441431\)
\(a_{96}=+0.768659796\) \(a_{97}=-1.071222978\) \(a_{98}=-0.484610215\) \(a_{99}=-0.706981693\) \(a_{100}=+0.691847203\)

Showing 100 of 5000 available coefficients

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