Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.7571888694 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.891841119\) \(a_{3}=+1.833208181\) \(a_{4}=-0.204619419\) \(a_{5}=+1.221132742\)
\(a_{6}=+1.634930435\) \(a_{7}=-0.126531276\) \(a_{8}=-1.074329130\) \(a_{9}=+2.360652236\) \(a_{10}=+1.089056390\)
\(a_{11}=-0.758162575\) \(a_{12}=-0.375109993\) \(a_{13}=+1.245833788\) \(a_{14}=-0.112845795\) \(a_{15}=+2.238590532\)
\(a_{16}=-0.753511474\) \(a_{17}=+0.095815409\) \(a_{18}=+2.105326731\) \(a_{19}=-0.229415734\) \(a_{20}=-0.249867472\)
\(a_{21}=-0.231958170\) \(a_{22}=-0.676160559\) \(a_{23}=-0.644965659\) \(a_{24}=-1.969468951\) \(a_{25}=+0.491165172\)
\(a_{26}=+1.111085799\) \(a_{27}=+2.494358812\) \(a_{28}=+0.025890756\) \(a_{29}=-1.840867775\) \(a_{30}=+1.996467084\)
\(a_{31}=+0.809019696\) \(a_{32}=+0.402316614\) \(a_{33}=-1.389869835\) \(a_{34}=+0.085452122\) \(a_{35}=-0.154511484\)
\(a_{36}=-0.483035289\) \(a_{37}=-1.677723845\) \(a_{38}=-0.204602385\) \(a_{39}=+2.283872692\) \(a_{40}=-1.311898476\)
\(a_{41}=+0.098801936\) \(a_{42}=-0.206869834\) \(a_{43}=-0.558251941\) \(a_{44}=+0.155134786\) \(a_{45}=+2.882669737\)
\(a_{46}=-0.575206895\) \(a_{47}=-0.043236586\) \(a_{48}=-1.381343400\) \(a_{49}=-0.983989836\) \(a_{50}=+0.438041296\)
\(a_{51}=+0.175649591\) \(a_{52}=-0.254921783\) \(a_{53}=-0.018025238\) \(a_{54}=+2.224571755\) \(a_{55}=-0.925817144\)
\(a_{56}=+0.135936231\) \(a_{57}=-0.420566789\) \(a_{58}=-1.641761590\) \(a_{59}=+0.796227492\) \(a_{60}=-0.458059088\)
\(a_{61}=+1.800908037\) \(a_{62}=+0.721517074\) \(a_{63}=-0.298696392\) \(a_{64}=+1.112313988\) \(a_{65}=+1.521328473\)
\(a_{66}=-1.239543161\) \(a_{67}=-0.344831844\) \(a_{68}=-0.019605693\) \(a_{69}=-1.182356322\) \(a_{70}=-0.137799694\)
\(a_{71}=+0.098909820\) \(a_{72}=-2.536117464\) \(a_{73}=-0.995098595\) \(a_{74}=-1.496263111\) \(a_{75}=+0.900408013\)
\(a_{76}=+0.046942914\) \(a_{77}=+0.095931277\) \(a_{78}=+2.036851576\) \(a_{79}=+0.189024155\) \(a_{80}=-0.920137531\)
\(a_{81}=+2.212026742\) \(a_{82}=+0.088115628\) \(a_{83}=+1.311765425\) \(a_{84}=+0.047463148\) \(a_{85}=+0.117003333\)
\(a_{86}=-0.497872042\) \(a_{87}=-3.374693862\) \(a_{88}=+0.814516143\) \(a_{89}=-0.761231769\) \(a_{90}=+2.570883400\)
\(a_{91}=-0.157636946\) \(a_{92}=+0.131972508\) \(a_{93}=+1.483101520\) \(a_{94}=-0.038560163\) \(a_{95}=-0.280147060\)
\(a_{96}=+0.737530091\) \(a_{97}=-0.236118502\) \(a_{98}=-0.877562623\) \(a_{99}=-1.789758181\) \(a_{100}=-0.100501929\)

Showing 100 of 1500 available coefficients

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