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: \( 23.246400292 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.869562160\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.614873300\) \(a_{7}=-0.574560882\) \(a_{8}=+0.353553391\) \(a_{9}=-0.243861650\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.892120705\) \(a_{12}=-0.434781080\) \(a_{13}=-0.595741729\) \(a_{14}=-0.406275896\) \(a_{15}=+0.388880020\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.268206217\) \(a_{18}=-0.172436226\) \(a_{19}=+0.725528406\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.499616402\) \(a_{22}=-1.337931381\) \(a_{23}=-1.520428424\) \(a_{24}=-0.307436650\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.421253017\) \(a_{27}=+1.081615023\) \(a_{28}=-0.287280441\) \(a_{29}=-0.346090392\) \(a_{30}=+0.274979699\)
\(a_{31}=-0.280258543\) \(a_{32}=+0.176776695\) \(a_{33}=+1.645316567\) \(a_{34}=-0.896757216\) \(a_{35}=+0.256951438\)
\(a_{36}=-0.121930825\) \(a_{37}=-0.061153215\) \(a_{38}=+0.513026056\) \(a_{39}=+0.518034465\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.855055734\) \(a_{42}=+0.353282146\) \(a_{43}=-0.616225496\) \(a_{44}=-0.946060352\) \(a_{45}=+0.109058245\)
\(a_{46}=-1.075105249\) \(a_{47}=-0.500235026\) \(a_{48}=-0.217390540\) \(a_{49}=-0.669879793\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.102784137\) \(a_{52}=-0.297870865\) \(a_{53}=+0.624614018\) \(a_{54}=+0.764817317\) \(a_{55}=+0.846182103\)
\(a_{56}=-0.203137948\) \(a_{57}=-0.630892047\) \(a_{58}=-0.244722863\) \(a_{59}=-1.759158920\) \(a_{60}=+0.194440010\)
\(a_{61}=+1.677460544\) \(a_{62}=-0.198172716\) \(a_{63}=+0.140113365\) \(a_{64}=+0.125000000\) \(a_{65}=+0.266423801\)
\(a_{66}=+1.163414502\) \(a_{67}=-0.377580534\) \(a_{68}=-0.634103109\) \(a_{69}=+1.322107024\) \(a_{70}=+0.181692104\)
\(a_{71}=-0.042951714\) \(a_{72}=-0.086218113\) \(a_{73}=+0.935260934\) \(a_{74}=-0.043241853\) \(a_{75}=-0.173912432\)
\(a_{76}=+0.362764203\) \(a_{77}=+1.087138541\) \(a_{78}=+0.366305683\) \(a_{79}=+1.043202036\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.696669846\) \(a_{82}=-1.311722489\) \(a_{83}=+0.560476955\) \(a_{84}=+0.249808201\) \(a_{85}=+0.567159062\)
\(a_{86}=-0.435737227\) \(a_{87}=+0.300947109\) \(a_{88}=-0.668965691\) \(a_{89}=-1.591915757\) \(a_{90}=+0.077115825\)
\(a_{91}=+0.342289893\) \(a_{92}=-0.760214212\) \(a_{93}=+0.243702224\) \(a_{94}=-0.353719579\) \(a_{95}=-0.324466167\)
\(a_{96}=-0.153718325\) \(a_{97}=-1.304840393\) \(a_{98}=-0.473676544\) \(a_{99}=+0.461415677\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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