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: \( 8.953063681 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.932667355\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.659495411\) \(a_{7}=+0.176261254\) \(a_{8}=+0.353553391\) \(a_{9}=-0.130131605\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.167368102\) \(a_{12}=-0.466333677\) \(a_{13}=-0.758909316\) \(a_{14}=+0.124635528\) \(a_{15}=-0.417101521\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.572128646\) \(a_{18}=-0.092016940\) \(a_{19}=-1.564365530\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.164393118\) \(a_{22}=-0.118347120\) \(a_{23}=-0.260928018\) \(a_{24}=-0.329747706\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.536629923\) \(a_{27}=+1.054036855\) \(a_{28}=+0.088130627\) \(a_{29}=-0.888899024\) \(a_{30}=-0.294935314\)
\(a_{31}=-0.323058359\) \(a_{32}=+0.176776695\) \(a_{33}=+0.156098765\) \(a_{34}=-1.111662826\) \(a_{35}=+0.078826429\)
\(a_{36}=-0.065065803\) \(a_{37}=+1.484102369\) \(a_{38}=-1.106173474\) \(a_{39}=+0.707809944\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.801012750\) \(a_{42}=-0.116243488\) \(a_{43}=-1.408299750\) \(a_{44}=-0.083684051\) \(a_{45}=-0.058196623\)
\(a_{46}=-0.184503971\) \(a_{47}=-1.133688313\) \(a_{48}=-0.233166839\) \(a_{49}=-0.968931970\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.466273066\) \(a_{52}=-0.379454658\) \(a_{53}=+0.783747286\) \(a_{54}=+0.745316608\) \(a_{55}=-0.074849291\)
\(a_{56}=+0.062317764\) \(a_{57}=+1.459032661\) \(a_{58}=-0.628546527\) \(a_{59}=-1.107437377\) \(a_{60}=-0.208550761\)
\(a_{61}=-0.078148531\) \(a_{62}=-0.228436756\) \(a_{63}=-0.022937160\) \(a_{64}=+0.125000000\) \(a_{65}=-0.339394564\)
\(a_{66}=+0.110378495\) \(a_{67}=+0.944980760\) \(a_{68}=-0.786064323\) \(a_{69}=+0.243359044\) \(a_{70}=+0.055738703\)
\(a_{71}=-1.219797277\) \(a_{72}=-0.046008470\) \(a_{73}=-0.090683015\) \(a_{74}=+1.049418849\) \(a_{75}=-0.186533471\)
\(a_{76}=-0.782182765\) \(a_{77}=-0.029500512\) \(a_{78}=+0.500497211\) \(a_{79}=+1.469824250\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.852934160\) \(a_{82}=+1.273508328\) \(a_{83}=+0.235716919\) \(a_{84}=-0.082196559\) \(a_{85}=-0.703077304\)
\(a_{86}=-0.995818303\) \(a_{87}=+0.829047101\) \(a_{88}=-0.059173560\) \(a_{89}=-0.360919026\) \(a_{90}=-0.041151227\)
\(a_{91}=-0.133766308\) \(a_{92}=-0.130464009\) \(a_{93}=+0.301305985\) \(a_{94}=-0.801638694\) \(a_{95}=-0.699605533\)
\(a_{96}=-0.164873853\) \(a_{97}=+1.166966190\) \(a_{98}=-0.685138367\) \(a_{99}=+0.021779880\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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