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: \( 15.6636752753 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.990071790\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.682884847\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.700086476\)
\(a_{11}=+0.117893206\) \(a_{12}=+0.000000000\) \(a_{13}=+1.670197219\) \(a_{14}=+1.189979287\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.129635146\) \(a_{18}=+0.000000000\) \(a_{19}=+1.066210462\) \(a_{20}=-0.495035895\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.083363085\) \(a_{23}=-1.246061192\) \(a_{24}=+0.000000000\) \(a_{25}=-0.019757851\)
\(a_{26}=+1.181007779\) \(a_{27}=+0.000000000\) \(a_{28}=+0.841442423\) \(a_{29}=-1.022692921\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.056108025\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.798772672\) \(a_{35}=-1.666176812\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.190926128\) \(a_{38}=+0.753924648\) \(a_{39}=+0.000000000\) \(a_{40}=-0.350043238\)
\(a_{41}=+0.977624974\) \(a_{42}=+0.000000000\) \(a_{43}=+0.394205203\) \(a_{44}=+0.058946603\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.881098318\) \(a_{47}=+0.590429531\) \(a_{48}=+0.000000000\) \(a_{49}=+1.832101407\) \(a_{50}=-0.013970910\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.835098610\) \(a_{53}=+1.202658858\) \(a_{54}=+0.000000000\) \(a_{55}=-0.116722737\)
\(a_{56}=+0.594989643\) \(a_{57}=+0.000000000\) \(a_{58}=-0.723153099\) \(a_{59}=+0.820608301\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.105676413\) \(a_{62}=+0.746781146\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-1.653615150\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.751936486\) \(a_{68}=-0.564817573\) \(a_{69}=+0.000000000\) \(a_{70}=-1.178164922\)
\(a_{71}=+1.823997863\) \(a_{72}=+0.000000000\) \(a_{73}=+0.279515335\) \(a_{74}=-0.135005160\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.533105231\) \(a_{77}=+0.198400690\) \(a_{78}=+0.000000000\) \(a_{79}=-0.968295035\) \(a_{80}=-0.247517947\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.691285249\) \(a_{83}=+0.632356739\) \(a_{84}=+0.000000000\) \(a_{85}=+1.118419891\)
\(a_{86}=+0.278745172\) \(a_{87}=+0.000000000\) \(a_{88}=+0.041681543\) \(a_{89}=-0.924656036\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.810749591\) \(a_{92}=-0.623030596\) \(a_{93}=+0.000000000\) \(a_{94}=+0.417496725\) \(a_{95}=-1.055624901\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.887562051\) \(a_{98}=+1.295491329\) \(a_{99}=+0.000000000\) \(a_{100}=-0.009878926\)

Showing 100 of 316 available coefficients

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