Properties

Level $18$
Weight $0$
Character 18.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 16.8455324231 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.551082614\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.711930441\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.389674253\)
\(a_{11}=+0.170766202\) \(a_{12}=+0.000000000\) \(a_{13}=+0.417731847\) \(a_{14}=-0.503410843\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.222519017\) \(a_{18}=+0.000000000\) \(a_{19}=+1.118700029\) \(a_{20}=-0.275541307\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.120749940\) \(a_{23}=+1.363993797\) \(a_{24}=+0.000000000\) \(a_{25}=-0.696307952\)
\(a_{26}=+0.295381021\) \(a_{27}=+0.000000000\) \(a_{28}=-0.355965221\) \(a_{29}=-0.759379082\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.314076653\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.157344706\) \(a_{35}=+0.392332489\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.431844496\) \(a_{38}=+0.791040376\) \(a_{39}=+0.000000000\) \(a_{40}=-0.194837127\)
\(a_{41}=-0.471552615\) \(a_{42}=+0.000000000\) \(a_{43}=+0.719826520\) \(a_{44}=+0.085383101\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.964489263\) \(a_{47}=+0.927638132\) \(a_{48}=+0.000000000\) \(a_{49}=-0.493155046\) \(a_{50}=-0.492364075\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.208865923\) \(a_{53}=-1.874971100\) \(a_{54}=+0.000000000\) \(a_{55}=-0.094106285\)
\(a_{56}=-0.251705421\) \(a_{57}=+0.000000000\) \(a_{58}=-0.536962098\) \(a_{59}=-1.076418888\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.159921690\) \(a_{62}=+0.222085731\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.230204758\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.475537328\) \(a_{68}=-0.111259508\) \(a_{69}=+0.000000000\) \(a_{70}=+0.277420963\)
\(a_{71}=-0.434469570\) \(a_{72}=+0.000000000\) \(a_{73}=+1.131875805\) \(a_{74}=-1.012466953\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.559350014\) \(a_{77}=-0.121573658\) \(a_{78}=+0.000000000\) \(a_{79}=+1.667303831\) \(a_{80}=-0.137770654\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.333438052\) \(a_{83}=+0.049911975\) \(a_{84}=+0.000000000\) \(a_{85}=+0.122626362\)
\(a_{86}=+0.508994214\) \(a_{87}=+0.000000000\) \(a_{88}=+0.060374970\) \(a_{89}=+0.201897587\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.297396018\) \(a_{92}=+0.681996899\) \(a_{93}=+0.000000000\) \(a_{94}=+0.655939214\) \(a_{95}=-0.616496136\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.794330629\) \(a_{98}=-0.348713278\) \(a_{99}=+0.000000000\) \(a_{100}=-0.348153976\)

Showing 100 of 330 available coefficients

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