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: \( 14.5407874029 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+1.361233057\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.037318386\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.962537125\)
\(a_{11}=-1.530340579\) \(a_{12}=+0.000000000\) \(a_{13}=-1.421083814\) \(a_{14}=+0.733494865\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.355480384\) \(a_{18}=+0.000000000\) \(a_{19}=-0.602245204\) \(a_{20}=+0.680616528\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.082114201\) \(a_{23}=-0.468814359\) \(a_{24}=+0.000000000\) \(a_{25}=+0.852955435\)
\(a_{26}=+1.004858002\) \(a_{27}=+0.000000000\) \(a_{28}=-0.518659193\) \(a_{29}=+0.873247432\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.224004948\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.958469371\) \(a_{35}=-1.412032077\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.879156827\) \(a_{38}=+0.425851668\) \(a_{39}=+0.000000000\) \(a_{40}=-0.481268563\)
\(a_{41}=-0.658993736\) \(a_{42}=+0.000000000\) \(a_{43}=+0.582996310\) \(a_{44}=-0.765170289\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.331501812\) \(a_{47}=-0.544976391\) \(a_{48}=+0.000000000\) \(a_{49}=+0.076029433\) \(a_{50}=-0.603130572\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.710541907\) \(a_{53}=-1.075983338\) \(a_{54}=+0.000000000\) \(a_{55}=-2.083150184\)
\(a_{56}=+0.366747432\) \(a_{57}=+0.000000000\) \(a_{58}=-0.617479181\) \(a_{59}=+1.159152057\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.038947068\) \(a_{62}=+0.158395418\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-1.934426264\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.050825732\) \(a_{68}=+0.677740192\) \(a_{69}=+0.000000000\) \(a_{70}=+0.998457457\)
\(a_{71}=-0.223155657\) \(a_{72}=+0.000000000\) \(a_{73}=+1.585715117\) \(a_{74}=-1.328764535\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.301122602\) \(a_{77}=+1.587450418\) \(a_{78}=+0.000000000\) \(a_{79}=+1.656394874\) \(a_{80}=+0.340308264\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.465978939\) \(a_{83}=+0.358475807\) \(a_{84}=+0.000000000\) \(a_{85}=+1.845124706\)
\(a_{86}=-0.412240644\) \(a_{87}=+0.000000000\) \(a_{88}=+0.541057100\) \(a_{89}=+0.064314073\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.474116368\) \(a_{92}=-0.234407180\) \(a_{93}=+0.000000000\) \(a_{94}=+0.385356501\) \(a_{95}=-0.819796080\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.658039198\) \(a_{98}=-0.053760928\) \(a_{99}=+0.000000000\) \(a_{100}=+0.426477717\)

Showing 100 of 292 available coefficients

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