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: \( 31.9896349188 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.495455785\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.057446927\) \(a_{7}=+1.331067784\) \(a_{8}=+0.353553391\) \(a_{9}=+1.236388005\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.221217441\) \(a_{12}=+0.747727892\) \(a_{13}=-1.660338509\) \(a_{14}=+0.941207056\) \(a_{15}=-0.668788159\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.117370667\) \(a_{18}=+0.874258342\) \(a_{19}=-0.872658302\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.990553017\) \(a_{22}=-0.156424353\) \(a_{23}=-1.011388710\) \(a_{24}=+0.528723463\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.174036619\) \(a_{27}=+0.353507809\) \(a_{28}=+0.665533892\) \(a_{29}=-1.340141994\) \(a_{30}=-0.472904642\)
\(a_{31}=-0.529871854\) \(a_{32}=+0.176776695\) \(a_{33}=-0.330820902\) \(a_{34}=-0.082993595\) \(a_{35}=-0.595271609\)
\(a_{36}=+0.618194002\) \(a_{37}=-1.875028641\) \(a_{38}=-0.617062603\) \(a_{39}=-2.482962828\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.276576389\) \(a_{42}=+1.407533537\) \(a_{43}=+0.536600781\) \(a_{44}=-0.110608721\) \(a_{45}=-0.552929525\)
\(a_{46}=-0.715159815\) \(a_{47}=+0.552919792\) \(a_{48}=+0.373863946\) \(a_{49}=+0.771741445\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.175522644\) \(a_{52}=-0.830169254\) \(a_{53}=-0.088198587\) \(a_{54}=+0.249967769\) \(a_{55}=+0.098931447\)
\(a_{56}=+0.470603528\) \(a_{57}=-1.305021906\) \(a_{58}=-0.947623492\) \(a_{59}=-0.725299046\) \(a_{60}=-0.334394079\)
\(a_{61}=+1.674936825\) \(a_{62}=-0.374675981\) \(a_{63}=+1.645716241\) \(a_{64}=+0.125000000\) \(a_{65}=+0.742525954\)
\(a_{66}=-0.233925703\) \(a_{67}=+0.507512874\) \(a_{68}=-0.058685334\) \(a_{69}=-1.512487097\) \(a_{70}=-0.420920592\)
\(a_{71}=+0.620064364\) \(a_{72}=+0.437129171\) \(a_{73}=-0.798042886\) \(a_{74}=-1.325845467\) \(a_{75}=+0.299091157\)
\(a_{76}=-0.436329151\) \(a_{77}=-0.294455409\) \(a_{78}=-1.755719853\) \(a_{79}=-1.419381794\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.707732706\) \(a_{82}=-0.902675821\) \(a_{83}=-0.240266585\) \(a_{84}=+0.995276509\) \(a_{85}=+0.052489758\)
\(a_{86}=+0.379434051\) \(a_{87}=-2.004123098\) \(a_{88}=-0.078212176\) \(a_{89}=+1.822858395\) \(a_{90}=-0.390980217\)
\(a_{91}=-2.210023099\) \(a_{92}=-0.505694355\) \(a_{93}=-0.792399929\) \(a_{94}=+0.390973334\) \(a_{95}=+0.390264657\)
\(a_{96}=+0.264361732\) \(a_{97}=-0.704797114\) \(a_{98}=+0.545703609\) \(a_{99}=-0.273510591\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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