Properties

Level $99$
Weight $0$
Character 99.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 99 = 3^{2} \cdot 11 \)
Weight: \( 0 \)
Character: 99.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.34690686208 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.941253520\) \(a_{3}=+0.000000000\) \(a_{4}=+2.768465228\) \(a_{5}=+0.735993316\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.862477790\) \(a_{8}=-3.433039350\) \(a_{9}=+0.000000000\) \(a_{10}=-1.428749616\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.000000000\) \(a_{13}=+0.274840490\) \(a_{14}=-3.615541565\) \(a_{15}=+0.000000000\)
\(a_{16}=+3.895934493\) \(a_{17}=+0.711849067\) \(a_{18}=+0.000000000\) \(a_{19}=+0.185579359\) \(a_{20}=+2.037571905\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.585309959\) \(a_{23}=-0.111253653\) \(a_{24}=+0.000000000\) \(a_{25}=-0.458313838\)
\(a_{26}=-0.533535068\) \(a_{27}=+0.000000000\) \(a_{28}=+5.156205000\) \(a_{29}=+0.441211051\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.736747494\) \(a_{32}=-4.129957198\) \(a_{33}=+0.000000000\) \(a_{34}=-1.381879507\) \(a_{35}=+1.370771205\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.411157480\) \(a_{38}=-0.360256585\) \(a_{39}=+0.000000000\) \(a_{40}=-2.526694016\)
\(a_{41}=+0.589857416\) \(a_{42}=+0.000000000\) \(a_{43}=+0.553464193\) \(a_{44}=+0.834723673\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.215971546\) \(a_{47}=+0.931578095\) \(a_{48}=+0.000000000\) \(a_{49}=+2.468823518\) \(a_{50}=+0.889703351\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.760886339\) \(a_{53}=-0.767893542\) \(a_{54}=+0.000000000\) \(a_{55}=+0.221910334\)
\(a_{56}=-6.393959540\) \(a_{57}=+0.000000000\) \(a_{58}=-0.856502506\) \(a_{59}=+1.120442742\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.335612039\) \(a_{62}=+1.430213666\) \(a_{63}=+0.000000000\) \(a_{64}=+4.121359454\) \(a_{65}=+0.202280764\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.547288741\) \(a_{68}=+1.970729390\) \(a_{69}=+0.000000000\) \(a_{70}=-2.661014428\)
\(a_{71}=-0.707948056\) \(a_{72}=+0.000000000\) \(a_{73}=+1.444096246\) \(a_{74}=+0.798160905\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.513770004\) \(a_{77}=+0.561558183\) \(a_{78}=+0.000000000\) \(a_{79}=-0.949176035\) \(a_{80}=+2.867381748\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.145062785\) \(a_{83}=+0.688694225\) \(a_{84}=+0.000000000\) \(a_{85}=+0.523916156\)
\(a_{86}=-1.074414313\) \(a_{87}=+0.000000000\) \(a_{88}=-1.035100310\) \(a_{89}=+1.029653783\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.511884308\) \(a_{92}=-0.308001870\) \(a_{93}=+0.000000000\) \(a_{94}=-1.808429256\) \(a_{95}=+0.136585169\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.941279122\) \(a_{98}=-4.792612343\) \(a_{99}=+0.000000000\) \(a_{100}=-1.268825925\)

Showing 100 of 808 available coefficients

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