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: \( 21.4872736484 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.307582137\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.924600196\) \(a_{7}=+0.203253895\) \(a_{8}=-0.353553391\) \(a_{9}=+0.709771045\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.808261363\) \(a_{12}=-0.653791068\) \(a_{13}=-0.109559114\) \(a_{14}=-0.143722208\) \(a_{15}=+0.584768509\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.895512161\) \(a_{18}=-0.501883919\) \(a_{19}=-0.405973435\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.265771163\) \(a_{22}=-1.278633872\) \(a_{23}=+1.777041472\) \(a_{24}=+0.462300098\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.077469992\) \(a_{27}=+0.379498198\) \(a_{28}=+0.101626948\) \(a_{29}=+0.865238473\) \(a_{30}=-0.413493778\)
\(a_{31}=+0.506767976\) \(a_{32}=-0.176776695\) \(a_{33}=-2.364450258\) \(a_{34}=-1.340329503\) \(a_{35}=-0.090897905\)
\(a_{36}=+0.354885522\) \(a_{37}=-0.338318605\) \(a_{38}=+0.287066569\) \(a_{39}=+0.143257540\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.630995189\) \(a_{42}=+0.187928591\) \(a_{43}=-0.640086307\) \(a_{44}=+0.904130682\) \(a_{45}=-0.317419261\)
\(a_{46}=-1.256558076\) \(a_{47}=+0.570213739\) \(a_{48}=-0.326895534\) \(a_{49}=-0.958687854\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.478537841\) \(a_{52}=-0.054779557\) \(a_{53}=+1.221329663\) \(a_{54}=-0.268345749\) \(a_{55}=-0.808679066\)
\(a_{56}=-0.071861104\) \(a_{57}=+0.530843612\) \(a_{58}=-0.611815992\) \(a_{59}=+0.035872501\) \(a_{60}=+0.292384254\)
\(a_{61}=-0.358559576\) \(a_{62}=-0.358339072\) \(a_{63}=+0.144263730\) \(a_{64}=+0.125000000\) \(a_{65}=+0.048996325\)
\(a_{66}=+1.671918811\) \(a_{67}=+0.670081703\) \(a_{68}=+0.947756080\) \(a_{69}=-2.323627686\) \(a_{70}=+0.064274525\)
\(a_{71}=-1.377886183\) \(a_{72}=-0.250941959\) \(a_{73}=-1.628380994\) \(a_{74}=+0.239227380\) \(a_{75}=-0.261516427\)
\(a_{76}=-0.202986717\) \(a_{77}=+0.367536166\) \(a_{78}=-0.101298378\) \(a_{79}=+0.157713340\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.205996109\) \(a_{82}=+0.446180977\) \(a_{83}=+1.167663301\) \(a_{84}=-0.132885581\) \(a_{85}=-0.847698809\)
\(a_{86}=+0.452609368\) \(a_{87}=-1.131370372\) \(a_{88}=-0.639316936\) \(a_{89}=+0.948037965\) \(a_{90}=+0.224449312\)
\(a_{91}=-0.022268317\) \(a_{92}=+0.888520736\) \(a_{93}=-0.662640753\) \(a_{94}=-0.403202002\) \(a_{95}=+0.181556840\)
\(a_{96}=+0.231150049\) \(a_{97}=+1.699031101\) \(a_{98}=+0.677894683\) \(a_{99}=+1.283451557\) \(a_{100}=+0.099975586\)

Showing 100 of 208 available coefficients

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