Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.329937903 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.853884090\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.310894012\) \(a_{7}=+1.457893541\) \(a_{8}=-0.353553391\) \(a_{9}=+2.436886220\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.621793851\) \(a_{12}=-0.926942045\) \(a_{13}=-0.095480959\) \(a_{14}=-1.030886409\) \(a_{15}=+0.829082170\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.920356956\) \(a_{18}=-1.723138771\) \(a_{19}=+1.394114827\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.702765641\) \(a_{22}=-0.439674649\) \(a_{23}=-0.780959691\) \(a_{24}=+0.655447006\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.067515234\) \(a_{27}=-2.663820502\) \(a_{28}=+0.728946771\) \(a_{29}=-0.537148336\) \(a_{30}=-0.586249624\)
\(a_{31}=-1.003740157\) \(a_{32}=-0.176776695\) \(a_{33}=-1.152733728\) \(a_{34}=-1.357897426\) \(a_{35}=-0.651989812\)
\(a_{36}=+1.218443110\) \(a_{37}=-1.001721734\) \(a_{38}=-0.985788048\) \(a_{39}=+0.177010631\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.423377475\) \(a_{42}=+1.911143913\) \(a_{43}=-0.785390626\) \(a_{44}=+0.310896926\) \(a_{45}=-1.089808648\)
\(a_{46}=+0.552221893\) \(a_{47}=+0.586028670\) \(a_{48}=-0.463471023\) \(a_{49}=+1.125453577\) \(a_{50}=-0.141421356\)
\(a_{51}=-3.560119208\) \(a_{52}=-0.047740480\) \(a_{53}=-1.456329996\) \(a_{54}=+1.883605541\) \(a_{55}=-0.278074664\)
\(a_{56}=-0.515443205\) \(a_{57}=-2.584527298\) \(a_{58}=+0.379821231\) \(a_{59}=+0.848619215\) \(a_{60}=+0.414541085\)
\(a_{61}=-0.226358057\) \(a_{62}=+0.709751472\) \(a_{63}=+3.552720680\) \(a_{64}=+0.125000000\) \(a_{65}=+0.042700383\)
\(a_{66}=+0.815105836\) \(a_{67}=+0.975627911\) \(a_{68}=+0.960178478\) \(a_{69}=+1.447808746\) \(a_{70}=+0.461026418\)
\(a_{71}=-1.197383409\) \(a_{72}=-0.861569385\) \(a_{73}=+0.146803925\) \(a_{74}=+0.708324231\) \(a_{75}=-0.370776818\)
\(a_{76}=+0.697057414\) \(a_{77}=+0.906509239\) \(a_{78}=-0.125165418\) \(a_{79}=-0.744627593\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.501528227\) \(a_{82}=-0.299373084\) \(a_{83}=+0.748409993\) \(a_{84}=-1.351382820\) \(a_{85}=-0.858809739\)
\(a_{86}=+0.555355037\) \(a_{87}=+0.995810754\) \(a_{88}=-0.219837324\) \(a_{89}=+0.121419545\) \(a_{90}=+0.770611085\)
\(a_{91}=-0.139201074\) \(a_{92}=-0.390479845\) \(a_{93}=+1.860817908\) \(a_{94}=-0.414384847\) \(a_{95}=-0.623467104\)
\(a_{96}=+0.327723503\) \(a_{97}=-1.243306491\) \(a_{98}=-0.795815856\) \(a_{99}=+1.515240867\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

Rows: Cols: