Properties

Level 10
Weight 0
Character 10.1
Symmetry even
Fricke sign -1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: \(-1\)
Spectral parameter: \( 30.610412682 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.683002998\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.482956052\) \(a_{7}=-0.283834597\) \(a_{8}=+0.353553391\) \(a_{9}=-0.533506904\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.652241746\) \(a_{12}=-0.341501499\) \(a_{13}=-1.842725037\) \(a_{14}=-0.200701368\) \(a_{15}=+0.305448227\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.396322197\) \(a_{18}=-0.377246350\) \(a_{19}=+0.312680147\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.193859881\) \(a_{22}=+0.461204562\) \(a_{23}=+0.757785070\) \(a_{24}=-0.241478026\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.303003370\) \(a_{27}=+1.047389814\) \(a_{28}=-0.141917299\) \(a_{29}=+0.525080071\) \(a_{30}=+0.215984512\)
\(a_{31}=-0.878757546\) \(a_{32}=+0.176776695\) \(a_{33}=-0.445483068\) \(a_{34}=+0.987348894\) \(a_{35}=+0.126934691\)
\(a_{36}=-0.266753452\) \(a_{37}=+0.313691013\) \(a_{38}=+0.221098252\) \(a_{39}=+1.258586726\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.850223192\) \(a_{42}=+0.137079636\) \(a_{43}=+1.405024818\) \(a_{44}=+0.326120873\) \(a_{45}=+0.238591541\)
\(a_{46}=+0.535834962\) \(a_{47}=+1.983730625\) \(a_{48}=-0.170750750\) \(a_{49}=-0.919437922\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.953692247\) \(a_{52}=-0.921362519\) \(a_{53}=-0.268202095\) \(a_{54}=+0.740616440\) \(a_{55}=-0.291691376\)
\(a_{56}=-0.100350684\) \(a_{57}=-0.213561478\) \(a_{58}=+0.371287679\) \(a_{59}=-0.595995951\) \(a_{60}=+0.152724113\)
\(a_{61}=-0.788880762\) \(a_{62}=-0.621375420\) \(a_{63}=+0.151427717\) \(a_{64}=+0.125000000\) \(a_{65}=+0.824091689\)
\(a_{66}=-0.315004099\) \(a_{67}=+0.403548562\) \(a_{68}=+0.698161098\) \(a_{69}=-0.517569475\) \(a_{70}=+0.089756381\)
\(a_{71}=-0.126080551\) \(a_{72}=-0.188623175\) \(a_{73}=+0.636546008\) \(a_{74}=+0.221813043\) \(a_{75}=-0.136600600\)
\(a_{76}=+0.156340073\) \(a_{77}=-0.185128773\) \(a_{78}=+0.889955209\) \(a_{79}=+1.536929631\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.181863479\) \(a_{82}=-1.308305366\) \(a_{83}=+0.683970237\) \(a_{84}=+0.096929940\) \(a_{85}=-0.624454270\)
\(a_{86}=+0.993502576\) \(a_{87}=-0.358631263\) \(a_{88}=+0.230602281\) \(a_{89}=+0.660228517\) \(a_{90}=+0.168709696\)
\(a_{91}=+0.523029118\) \(a_{92}=+0.378892535\) \(a_{93}=+0.600194039\) \(a_{94}=+1.402709377\) \(a_{95}=-0.139834813\)
\(a_{96}=-0.120739013\) \(a_{97}=-1.170580371\) \(a_{98}=-0.650140789\) \(a_{99}=-0.347975475\) \(a_{100}=+0.099975586\)

Showing 100 of 252 available coefficients

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