Properties

Level $61$
Weight $0$
Character 61.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 1.40716257846 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.543109797\) \(a_{3}=-0.134738930\) \(a_{4}=-0.705031749\) \(a_{5}=-0.388268554\)
\(a_{6}=+0.073178033\) \(a_{7}=-1.154524263\) \(a_{8}=+0.926019447\) \(a_{9}=-0.981845421\) \(a_{10}=+0.210872455\)
\(a_{11}=+0.525841690\) \(a_{12}=+0.094995224\) \(a_{13}=+0.026717567\) \(a_{14}=+0.627033438\) \(a_{15}=+0.052314890\)
\(a_{16}=+0.202101515\) \(a_{17}=-0.371807628\) \(a_{18}=+0.533249867\) \(a_{19}=+0.777749765\) \(a_{20}=+0.273741657\)
\(a_{21}=+0.155559364\) \(a_{22}=-0.285589774\) \(a_{23}=+0.065143952\) \(a_{24}=-0.124770870\) \(a_{25}=-0.849247530\)
\(a_{26}=-0.014510572\) \(a_{27}=+0.267031732\) \(a_{28}=+0.813976260\) \(a_{29}=-0.768070742\) \(a_{30}=-0.028412729\)
\(a_{31}=-1.542820549\) \(a_{32}=-1.035782759\) \(a_{33}=-0.070851347\) \(a_{34}=+0.201932365\) \(a_{35}=+0.448265466\)
\(a_{36}=+0.692232194\) \(a_{37}=-1.503724803\) \(a_{38}=-0.422403517\) \(a_{39}=-0.003599896\) \(a_{40}=-0.359544231\)
\(a_{41}=+0.050501043\) \(a_{42}=-0.084485815\) \(a_{43}=+1.656253073\) \(a_{44}=-0.370735086\) \(a_{45}=+0.381219702\)
\(a_{46}=-0.035380318\) \(a_{47}=+0.286428485\) \(a_{48}=-0.027230942\) \(a_{49}=+0.332926274\) \(a_{50}=+0.461234654\)
\(a_{51}=+0.050096962\) \(a_{52}=-0.018836733\) \(a_{53}=+1.490937563\) \(a_{54}=-0.145027550\) \(a_{55}=-0.204167793\)
\(a_{56}=-1.069111919\) \(a_{57}=-0.104793172\) \(a_{58}=+0.417146745\) \(a_{59}=-1.357507403\) \(a_{60}=-0.036883658\)
\(a_{61}=-0.128036880\) \(a_{62}=+0.837920955\) \(a_{63}=+1.133564361\) \(a_{64}=+0.360442249\) \(a_{65}=-0.010373591\)
\(a_{66}=+0.038480061\) \(a_{67}=+0.960129541\) \(a_{68}=+0.262136182\) \(a_{69}=-0.008777426\) \(a_{70}=-0.243457366\)
\(a_{71}=+0.360054363\) \(a_{72}=-0.909207953\) \(a_{73}=-0.530590374\) \(a_{74}=+0.816687672\) \(a_{75}=+0.114426704\)
\(a_{76}=-0.548338277\) \(a_{77}=-0.607096990\) \(a_{78}=+0.001955139\) \(a_{79}=-1.433372434\) \(a_{80}=-0.078469663\)
\(a_{81}=+0.945865851\) \(a_{82}=-0.027427611\) \(a_{83}=-0.784679038\) \(a_{84}=-0.109674291\) \(a_{85}=+0.144361210\)
\(a_{86}=-0.899527270\) \(a_{87}=+0.103489030\) \(a_{88}=+0.486939631\) \(a_{89}=+1.211100300\) \(a_{90}=-0.207044155\)
\(a_{91}=-0.030846080\) \(a_{92}=-0.045928554\) \(a_{93}=+0.207877991\) \(a_{94}=-0.155562116\) \(a_{95}=-0.301975776\)
\(a_{96}=+0.139560261\) \(a_{97}=+0.550539047\) \(a_{98}=-0.180815521\) \(a_{99}=-0.516295255\) \(a_{100}=+0.598746471\)

Showing 100 of 546 available coefficients

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