Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 17.8780025394 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.982568571\) \(a_{4}=+0.500000000\) \(a_{5}=+1.811756323\)
\(a_{6}=-0.694780900\) \(a_{7}=+0.008210929\) \(a_{8}=-0.353553391\) \(a_{9}=-0.034559003\) \(a_{10}=-1.281105182\)
\(a_{11}=-0.174752307\) \(a_{12}=+0.491284286\) \(a_{13}=+1.101799131\) \(a_{14}=-0.005806004\) \(a_{15}=+1.780174821\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.660345344\) \(a_{18}=+0.024436906\) \(a_{19}=-0.143219875\) \(a_{20}=+0.905878161\)
\(a_{21}=+0.008067801\) \(a_{22}=+0.123568541\) \(a_{23}=-0.940259624\) \(a_{24}=-0.347390450\) \(a_{25}=+2.282460973\)
\(a_{26}=-0.779089637\) \(a_{27}=-1.016525161\) \(a_{28}=+0.004105465\) \(a_{29}=+0.983664688\) \(a_{30}=-1.258773688\)
\(a_{31}=+1.347574850\) \(a_{32}=-0.176776695\) \(a_{33}=-0.171706125\) \(a_{34}=-0.466934670\) \(a_{35}=+0.014876203\)
\(a_{36}=-0.017279502\) \(a_{37}=+0.055959378\) \(a_{38}=+0.101271745\) \(a_{39}=+1.082593197\) \(a_{40}=-0.640552591\)
\(a_{41}=-0.582182943\) \(a_{42}=-0.005704797\) \(a_{43}=-0.055556049\) \(a_{44}=-0.087376154\) \(a_{45}=-0.062612493\)
\(a_{46}=+0.664863956\) \(a_{47}=+0.718199639\) \(a_{48}=+0.245642143\) \(a_{49}=-0.999932581\) \(a_{50}=-1.613943632\)
\(a_{51}=+0.648834581\) \(a_{52}=+0.550899565\) \(a_{53}=+0.251360647\) \(a_{54}=+0.718791835\) \(a_{55}=-0.316608597\)
\(a_{56}=-0.002903002\) \(a_{57}=-0.140723348\) \(a_{58}=-0.695555972\) \(a_{59}=-0.135518934\) \(a_{60}=+0.890087411\)
\(a_{61}=-0.122286860\) \(a_{62}=-0.952879314\) \(a_{63}=-0.000283762\) \(a_{64}=+0.125000000\) \(a_{65}=+1.996191542\)
\(a_{66}=+0.121414565\) \(a_{67}=-1.567974528\) \(a_{68}=+0.330172672\) \(a_{69}=-0.923869555\) \(a_{70}=-0.010519064\)
\(a_{71}=+0.622194481\) \(a_{72}=+0.012218453\) \(a_{73}=-0.958838500\) \(a_{74}=-0.039569256\) \(a_{75}=+2.242674417\)
\(a_{76}=-0.071609937\) \(a_{77}=-0.001434879\) \(a_{78}=-0.765508991\) \(a_{79}=-0.777381901\) \(a_{80}=+0.452939081\)
\(a_{81}=-0.964246672\) \(a_{82}=+0.411665507\) \(a_{83}=-0.340581818\) \(a_{84}=+0.004033900\) \(a_{85}=+1.196384851\)
\(a_{86}=+0.039284059\) \(a_{87}=+0.966518007\) \(a_{88}=+0.061784271\) \(a_{89}=-1.760006252\) \(a_{90}=+0.044273718\)
\(a_{91}=+0.009046795\) \(a_{92}=-0.470129812\) \(a_{93}=+1.324084694\) \(a_{94}=-0.507843835\) \(a_{95}=-0.259479514\)
\(a_{96}=-0.173695225\) \(a_{97}=-0.732306331\) \(a_{98}=+0.707059109\) \(a_{99}=+0.006039266\) \(a_{100}=+1.141230487\)

Showing 100 of 1228 available coefficients

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