Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.6192194385 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.310058595\) \(a_{3}=-0.577350269\) \(a_{4}=+0.716253522\) \(a_{5}=-0.665951956\)
\(a_{6}=+0.756362682\) \(a_{7}=-1.751531374\) \(a_{8}=+0.371724512\) \(a_{9}=+0.333333333\) \(a_{10}=+0.872436084\)
\(a_{11}=-0.301511345\) \(a_{12}=-0.413529164\) \(a_{13}=+0.361608455\) \(a_{14}=+2.294608731\) \(a_{15}=+0.384487541\)
\(a_{16}=-1.203234414\) \(a_{17}=+1.422913150\) \(a_{18}=-0.436686198\) \(a_{19}=-1.204231680\) \(a_{20}=-0.476990434\)
\(a_{21}=+1.011247110\) \(a_{22}=+0.394997528\) \(a_{23}=+0.120774782\) \(a_{24}=-0.214615247\) \(a_{25}=-0.556507992\)
\(a_{26}=-0.473728264\) \(a_{27}=-0.192450090\) \(a_{28}=-1.254540516\) \(a_{29}=+0.574482940\) \(a_{30}=-0.503701208\)
\(a_{31}=+1.009662132\) \(a_{32}=+1.204583074\) \(a_{33}=+0.174077656\) \(a_{34}=-1.864099602\) \(a_{35}=+1.166435745\)
\(a_{36}=+0.238751174\) \(a_{37}=+1.252474793\) \(a_{38}=+1.577614062\) \(a_{39}=-0.208774739\) \(a_{40}=-0.247550666\)
\(a_{41}=-1.393876610\) \(a_{42}=-1.324792969\) \(a_{43}=-0.805466747\) \(a_{44}=-0.215958562\) \(a_{45}=-0.221983985\)
\(a_{46}=-0.158222041\) \(a_{47}=+0.367263633\) \(a_{48}=+0.694687713\) \(a_{49}=+2.067862155\) \(a_{50}=+0.729058078\)
\(a_{51}=-0.821519290\) \(a_{52}=+0.259003329\) \(a_{53}=-0.080288617\) \(a_{54}=+0.252120894\) \(a_{55}=+0.200792070\)
\(a_{56}=-0.651087146\) \(a_{57}=+0.695263484\) \(a_{58}=-0.752606313\) \(a_{59}=-0.375837892\) \(a_{60}=+0.275390556\)
\(a_{61}=-0.903763879\) \(a_{62}=-1.322716553\) \(a_{63}=-0.583843791\) \(a_{64}=-0.374839995\) \(a_{65}=-0.240813858\)
\(a_{66}=-0.228051929\) \(a_{67}=+1.488527424\) \(a_{68}=+1.019166555\) \(a_{69}=-0.069729353\) \(a_{70}=-1.528099174\)
\(a_{71}=+0.667820563\) \(a_{72}=+0.123908171\) \(a_{73}=+0.505690609\) \(a_{74}=-1.640815368\) \(a_{75}=+0.321300039\)
\(a_{76}=-0.862535182\) \(a_{77}=+0.528106580\) \(a_{78}=+0.273507141\) \(a_{79}=-0.681675140\) \(a_{80}=+0.801296312\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.826060033\) \(a_{83}=+1.655943310\) \(a_{84}=+0.724309304\) \(a_{85}=-0.947591796\)
\(a_{86}=+1.055208635\) \(a_{87}=-0.331677880\) \(a_{88}=-0.112079158\) \(a_{89}=+1.159261015\) \(a_{90}=+0.290812028\)
\(a_{91}=-0.633368553\) \(a_{92}=+0.086505363\) \(a_{93}=-0.582928703\) \(a_{94}=-0.481136879\) \(a_{95}=+0.801960443\)
\(a_{96}=-0.695466362\) \(a_{97}=+1.105359075\) \(a_{98}=-2.709020589\) \(a_{99}=-0.100503782\) \(a_{100}=-0.398600809\)

Showing 100 of 330 available coefficients

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