Properties

Level $491$
Weight $0$
Character 491.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 491 \)
Weight: \( 0 \)
Character: 491.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.8256765558 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.419609714\) \(a_{3}=-0.483344747\) \(a_{4}=+1.015291907\) \(a_{5}=+0.467652973\)
\(a_{6}=-0.686160537\) \(a_{7}=+0.580588670\) \(a_{8}=+0.021708217\) \(a_{9}=-0.766378169\) \(a_{10}=+0.663884771\)
\(a_{11}=-1.182761849\) \(a_{12}=-0.490735917\) \(a_{13}=+0.562623862\) \(a_{14}=+0.824209322\) \(a_{15}=-0.226037543\)
\(a_{16}=-0.984474268\) \(a_{17}=+1.064231206\) \(a_{18}=-1.087957935\) \(a_{19}=+0.749903002\) \(a_{20}=+0.474804226\)
\(a_{21}=-0.280624228\) \(a_{22}=-1.679060433\) \(a_{23}=-0.438200450\) \(a_{24}=-0.010492324\) \(a_{25}=-0.781300896\)
\(a_{26}=+0.798706248\) \(a_{27}=+0.853769224\) \(a_{28}=+0.589466751\) \(a_{29}=-0.063140796\) \(a_{30}=-0.320884819\)
\(a_{31}=+0.729137115\) \(a_{32}=-1.419278039\) \(a_{33}=+0.571681492\) \(a_{34}=+1.510792612\) \(a_{35}=+0.271513897\)
\(a_{36}=-0.778097292\) \(a_{37}=-1.029954264\) \(a_{38}=+1.064569628\) \(a_{39}=-0.271941234\) \(a_{40}=+0.010151906\)
\(a_{41}=+0.467713298\) \(a_{42}=-0.398376914\) \(a_{43}=+0.690733180\) \(a_{44}=-1.200848275\) \(a_{45}=-0.358398859\)
\(a_{46}=-0.622073996\) \(a_{47}=-0.007322119\) \(a_{48}=+0.475840202\) \(a_{49}=-0.662917064\) \(a_{50}=-1.109141961\)
\(a_{51}=-0.514390448\) \(a_{52}=+0.571227338\) \(a_{53}=+1.425774667\) \(a_{54}=+1.212018900\) \(a_{55}=-0.553122121\)
\(a_{56}=+0.012603613\) \(a_{57}=-0.362461579\) \(a_{58}=-0.089635482\) \(a_{59}=+1.426223974\) \(a_{60}=-0.229494154\)
\(a_{61}=-1.006949649\) \(a_{62}=+1.035090106\) \(a_{63}=-0.444950315\) \(a_{64}=-1.030345957\) \(a_{65}=+0.263112832\)
\(a_{66}=+0.811564759\) \(a_{67}=+0.088754638\) \(a_{68}=+1.080505368\) \(a_{69}=+0.211801748\) \(a_{70}=+0.385443918\)
\(a_{71}=+1.013835469\) \(a_{72}=-0.016636825\) \(a_{73}=+0.654071043\) \(a_{74}=-1.462133318\) \(a_{75}=+0.377637394\)
\(a_{76}=+0.761370421\) \(a_{77}=-0.686698026\) \(a_{78}=-0.386050408\) \(a_{79}=+0.385613281\) \(a_{80}=-0.460392337\)
\(a_{81}=+0.353713262\) \(a_{82}=+0.663970706\) \(a_{83}=+0.099470763\) \(a_{84}=-0.284915522\) \(a_{85}=+0.497690982\)
\(a_{86}=+0.980571545\) \(a_{87}=+0.030518728\) \(a_{88}=-0.025675954\) \(a_{89}=-0.534336696\) \(a_{90}=-0.508786641\)
\(a_{91}=+0.326653079\) \(a_{92}=-0.444901183\) \(a_{93}=-0.352424470\) \(a_{94}=-0.010394834\) \(a_{95}=+0.350694350\)
\(a_{96}=+0.686000402\) \(a_{97}=-0.889939395\) \(a_{98}=-0.941083389\) \(a_{99}=+0.906442828\) \(a_{100}=-0.793248447\)

Showing 100 of 1486 available coefficients

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