Properties

Level $18$
Weight $0$
Character 18.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.98851274234 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.031621534\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.801624174\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.022359801\)
\(a_{11}=+1.334290434\) \(a_{12}=+0.000000000\) \(a_{13}=+0.924263095\) \(a_{14}=+0.566833889\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.166410164\) \(a_{18}=+0.000000000\) \(a_{19}=-1.608480791\) \(a_{20}=-0.015810767\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.943485814\) \(a_{23}=+1.481229025\) \(a_{24}=+0.000000000\) \(a_{25}=-0.999000079\)
\(a_{26}=-0.653552702\) \(a_{27}=+0.000000000\) \(a_{28}=-0.400812087\) \(a_{29}=-0.651287359\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.804384166\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.117669755\) \(a_{35}=+0.025348586\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.302805915\) \(a_{38}=+1.137367675\) \(a_{39}=+0.000000000\) \(a_{40}=+0.011179901\)
\(a_{41}=-0.201203425\) \(a_{42}=+0.000000000\) \(a_{43}=+0.406133537\) \(a_{44}=+0.667145217\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.047387088\) \(a_{47}=-1.384171303\) \(a_{48}=+0.000000000\) \(a_{49}=-0.357398684\) \(a_{50}=+0.706399730\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.462131548\) \(a_{53}=-1.773010293\) \(a_{54}=+0.000000000\) \(a_{55}=-0.042192310\)
\(a_{56}=+0.283416945\) \(a_{57}=+0.000000000\) \(a_{58}=+0.460529708\) \(a_{59}=+0.761233914\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.004247934\) \(a_{62}=+1.275892280\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.029226617\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.038347353\) \(a_{68}=-0.083205082\) \(a_{69}=+0.000000000\) \(a_{70}=-0.017924157\)
\(a_{71}=-0.404997581\) \(a_{72}=+0.000000000\) \(a_{73}=+0.608177442\) \(a_{74}=+0.214116116\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.804240395\) \(a_{77}=-1.069599467\) \(a_{78}=+0.000000000\) \(a_{79}=+1.174135008\) \(a_{80}=-0.007905383\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.142272306\) \(a_{83}=-0.740494294\) \(a_{84}=+0.000000000\) \(a_{85}=+0.005262145\)
\(a_{86}=-0.287179778\) \(a_{87}=+0.000000000\) \(a_{88}=-0.471742907\) \(a_{89}=+0.999130431\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.740911640\) \(a_{92}=+0.740614513\) \(a_{93}=+0.000000000\) \(a_{94}=+0.978756914\) \(a_{95}=+0.050862630\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.914732940\) \(a_{98}=+0.252719033\) \(a_{99}=+0.000000000\) \(a_{100}=-0.499500039\)

Showing 100 of 226 available coefficients

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