Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 21.6168116132 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.032205205\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.022772519\) \(a_{7}=-1.312980222\) \(a_{8}=-0.353553391\) \(a_{9}=-0.998962825\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.473878824\) \(a_{12}=-0.016102602\) \(a_{13}=+1.288404596\) \(a_{14}=+0.928417219\) \(a_{15}=+0.014402605\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.091153845\) \(a_{18}=+0.706373388\) \(a_{19}=+0.995961564\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.042284797\) \(a_{22}=+0.335082930\) \(a_{23}=+0.286581366\) \(a_{24}=+0.011386259\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.911039627\) \(a_{27}=+0.064377007\) \(a_{28}=-0.656490111\) \(a_{29}=+0.268955577\) \(a_{30}=-0.010184180\)
\(a_{31}=+0.271730126\) \(a_{32}=-0.176776695\) \(a_{33}=+0.015261365\) \(a_{34}=-0.064455502\) \(a_{35}=+0.587182606\)
\(a_{36}=-0.499481412\) \(a_{37}=+0.400090166\) \(a_{38}=-0.704251175\) \(a_{39}=-0.041493334\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.321292632\) \(a_{42}=-0.029899867\) \(a_{43}=-1.592696438\) \(a_{44}=-0.236939412\) \(a_{45}=+0.446749757\)
\(a_{46}=-0.202643627\) \(a_{47}=+1.659786713\) \(a_{48}=-0.008051301\) \(a_{49}=+0.723917064\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.002935628\) \(a_{52}=+0.644202298\) \(a_{53}=+1.767526577\) \(a_{54}=-0.045521418\) \(a_{55}=+0.211925053\)
\(a_{56}=+0.464208609\) \(a_{57}=-0.032075146\) \(a_{58}=-0.190180312\) \(a_{59}=-1.080771655\) \(a_{60}=+0.007201303\)
\(a_{61}=-0.553412649\) \(a_{62}=-0.192142214\) \(a_{63}=+1.311618432\) \(a_{64}=+0.125000000\) \(a_{65}=-0.576192052\)
\(a_{66}=-0.010791414\) \(a_{67}=+0.238257428\) \(a_{68}=+0.045576922\) \(a_{69}=-0.009229412\) \(a_{70}=-0.415200802\)
\(a_{71}=+1.748119907\) \(a_{72}=+0.353186694\) \(a_{73}=-1.280364186\) \(a_{74}=-0.282906470\) \(a_{75}=-0.006441041\)
\(a_{76}=+0.497980782\) \(a_{77}=+0.622193524\) \(a_{78}=+0.029340218\) \(a_{79}=+1.687504106\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.996889550\) \(a_{82}=+0.227188199\) \(a_{83}=-0.563956711\) \(a_{84}=+0.021142398\) \(a_{85}=-0.040765239\)
\(a_{86}=+1.126206451\) \(a_{87}=-0.008661769\) \(a_{88}=+0.167541465\) \(a_{89}=-0.443270447\) \(a_{90}=-0.315899782\)
\(a_{91}=-1.691649753\) \(a_{92}=+0.143290683\) \(a_{93}=-0.008751124\) \(a_{94}=-1.173646440\) \(a_{95}=-0.445407552\)
\(a_{96}=+0.005693130\) \(a_{97}=-0.410748497\) \(a_{98}=-0.511886665\) \(a_{99}=+0.473387329\) \(a_{100}=+0.099975586\)

Showing 100 of 208 available coefficients

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