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: \( 23.638281764 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.349380819\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.247049546\) \(a_{7}=-0.588930959\) \(a_{8}=+0.353553391\) \(a_{9}=-0.877933044\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.057436446\) \(a_{12}=-0.174690409\) \(a_{13}=+1.009537889\) \(a_{14}=-0.416437075\) \(a_{15}=+0.156247852\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.085531240\) \(a_{18}=-0.620792409\) \(a_{19}=+0.252109669\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.205761181\) \(a_{22}=-0.040613700\) \(a_{23}=+1.245672781\) \(a_{24}=-0.123524773\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.713851087\) \(a_{27}=+0.656113784\) \(a_{28}=-0.294465479\) \(a_{29}=-1.318929339\) \(a_{30}=+0.110483916\)
\(a_{31}=-0.119216808\) \(a_{32}=+0.176776695\) \(a_{33}=+0.020067192\) \(a_{34}=+0.767586501\) \(a_{35}=+0.263377932\)
\(a_{36}=-0.438966522\) \(a_{37}=-1.574367063\) \(a_{38}=+0.178268456\) \(a_{39}=-0.352713174\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.413247622\) \(a_{42}=+0.145495126\) \(a_{43}=+1.346517298\) \(a_{44}=-0.028718223\) \(a_{45}=+0.392623593\)
\(a_{46}=+0.880823670\) \(a_{47}=+0.818844195\) \(a_{48}=-0.087345205\) \(a_{49}=-0.653160326\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.379263793\) \(a_{52}=+0.504768945\) \(a_{53}=-0.282479303\) \(a_{54}=+0.463942506\) \(a_{55}=+0.025686359\)
\(a_{56}=-0.208218537\) \(a_{57}=-0.088082283\) \(a_{58}=-0.932623879\) \(a_{59}=-1.218130233\) \(a_{60}=+0.078123926\)
\(a_{61}=+0.284532101\) \(a_{62}=-0.084299013\) \(a_{63}=+0.517041949\) \(a_{64}=+0.125000000\) \(a_{65}=-0.451479069\)
\(a_{66}=+0.014189648\) \(a_{67}=+0.096390390\) \(a_{68}=+0.542765620\) \(a_{69}=-0.435214176\) \(a_{70}=+0.186236321\)
\(a_{71}=-1.289194807\) \(a_{72}=-0.310396204\) \(a_{73}=-0.191470886\) \(a_{74}=-1.113245626\) \(a_{75}=-0.069876164\)
\(a_{76}=+0.126054834\) \(a_{77}=+0.033826101\) \(a_{78}=-0.249405877\) \(a_{79}=-1.853846584\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.648699473\) \(a_{82}=-0.292210196\) \(a_{83}=-0.239042491\) \(a_{84}=+0.102880590\) \(a_{85}=-0.485464329\)
\(a_{86}=+0.952131513\) \(a_{87}=+0.460808612\) \(a_{88}=-0.020306850\) \(a_{89}=+0.397409610\) \(a_{90}=+0.277626805\)
\(a_{91}=-0.594548117\) \(a_{92}=+0.622836390\) \(a_{93}=+0.041652066\) \(a_{94}=+0.579010283\) \(a_{95}=-0.112746871\)
\(a_{96}=-0.061762387\) \(a_{97}=+0.857048609\) \(a_{98}=-0.461854095\) \(a_{99}=+0.050425353\) \(a_{100}=+0.099975586\)

Showing 100 of 218 available coefficients

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