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: \( 9.23048002425 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.386468724\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.273274656\) \(a_{7}=-1.386243657\) \(a_{8}=+0.353553391\) \(a_{9}=-0.850641925\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.241795037\) \(a_{12}=+0.193234362\) \(a_{13}=-0.954603628\) \(a_{14}=-0.980222290\) \(a_{15}=-0.172834068\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.354415910\) \(a_{18}=-0.601494674\) \(a_{19}=-0.284334632\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.535739818\) \(a_{22}=+0.878081692\) \(a_{23}=-1.485073239\) \(a_{24}=+0.136637328\) \(a_{25}=+0.200000000\)
\(a_{26}=-0.675006699\) \(a_{27}=-0.715215224\) \(a_{28}=-0.693121829\) \(a_{29}=+0.087512786\) \(a_{30}=-0.122212141\)
\(a_{31}=+1.373238441\) \(a_{32}=+0.176776696\) \(a_{33}=+0.479914944\) \(a_{34}=-0.957716679\) \(a_{35}=+0.619947011\)
\(a_{36}=-0.425320952\) \(a_{37}=-0.052733402\) \(a_{38}=-0.201054963\) \(a_{39}=-0.368924417\) \(a_{40}=-0.158113882\)
\(a_{41}=-0.945849609\) \(a_{42}=-0.378825175\) \(a_{43}=+0.727763256\) \(a_{44}=+0.620897519\) \(a_{45}=+0.380418634\)
\(a_{46}=-1.050105358\) \(a_{47}=+1.122372411\) \(a_{48}=+0.096617181\) \(a_{49}=+0.921671477\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.523439389\) \(a_{52}=-0.477301814\) \(a_{53}=+0.749496101\) \(a_{54}=-0.505733534\) \(a_{55}=-0.555347624\)
\(a_{56}=-0.490111146\) \(a_{57}=-0.109886442\) \(a_{58}=+0.061880885\) \(a_{59}=-0.711404125\) \(a_{60}=-0.086417034\)
\(a_{61}=-0.773018090\) \(a_{62}=+0.971026215\) \(a_{63}=+1.179196971\) \(a_{64}=+0.124999998\) \(a_{65}=+0.426911729\)
\(a_{66}=+0.339351108\) \(a_{67}=-0.392531348\) \(a_{68}=-0.677207946\) \(a_{69}=-0.573934367\) \(a_{70}=+0.438368732\)
\(a_{71}=+1.176356408\) \(a_{72}=-0.300747335\) \(a_{73}=+0.262171342\) \(a_{74}=-0.037288175\) \(a_{75}=+0.077293664\)
\(a_{76}=-0.142167184\) \(a_{77}=-1.721430492\) \(a_{78}=-0.260868977\) \(a_{79}=+1.430689039\) \(a_{80}=-0.111803397\)
\(a_{81}=+0.574233613\) \(a_{82}=-0.668816634\) \(a_{83}=-1.191251196\) \(a_{84}=-0.267869901\) \(a_{85}=+0.605713207\)
\(a_{86}=+0.514606327\) \(a_{87}=+0.033820968\) \(a_{88}=+0.439040839\) \(a_{89}=-1.940876184\) \(a_{90}=+0.268996622\)
\(a_{91}=+1.323313217\) \(a_{92}=-0.742536644\) \(a_{93}=+0.530713768\) \(a_{94}=+0.793637123\) \(a_{95}=+0.127158230\)
\(a_{96}=+0.068318763\) \(a_{97}=+0.153770980\) \(a_{98}=+0.651720017\) \(a_{99}=-1.056322754\) \(a_{100}=+0.100000083\)

Showing 100 of 2000 available coefficients

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