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: \( 4.39865050004 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.845582386\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.706714691\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.597917039\)
\(a_{11}=+1.301407767\) \(a_{12}=+0.000000000\) \(a_{13}=+0.081906110\) \(a_{14}=-1.206829532\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.155586017\) \(a_{18}=+0.000000000\) \(a_{19}=+0.812367811\) \(a_{20}=-0.422791193\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.920234257\) \(a_{23}=+1.473415692\) \(a_{24}=+0.000000000\) \(a_{25}=-0.284990429\)
\(a_{26}=-0.057916366\) \(a_{27}=+0.000000000\) \(a_{28}=+0.853357346\) \(a_{29}=+0.045378970\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.018859736\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.110015928\) \(a_{35}=-1.443167880\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.770076818\) \(a_{38}=-0.574430788\) \(a_{39}=+0.000000000\) \(a_{40}=+0.298958519\)
\(a_{41}=+1.374924163\) \(a_{42}=+0.000000000\) \(a_{43}=+0.107738477\) \(a_{44}=+0.650703883\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.041862228\) \(a_{47}=-0.107339948\) \(a_{48}=+0.000000000\) \(a_{49}=+1.912875037\) \(a_{50}=+0.201518665\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.040953055\) \(a_{53}=+0.972747870\) \(a_{54}=+0.000000000\) \(a_{55}=-1.100447484\)
\(a_{56}=-0.603414766\) \(a_{57}=+0.000000000\) \(a_{58}=-0.032087778\) \(a_{59}=-1.764962532\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.487287470\) \(a_{62}=-0.013335847\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.069258364\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.619053900\) \(a_{68}=-0.077793008\) \(a_{69}=+0.000000000\) \(a_{70}=+1.020473794\)
\(a_{71}=-0.161407900\) \(a_{72}=+0.000000000\) \(a_{73}=-1.336952500\) \(a_{74}=+0.544526540\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.406183905\) \(a_{77}=+2.221131755\) \(a_{78}=+0.000000000\) \(a_{79}=+0.526593000\) \(a_{80}=-0.211395596\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.972218199\) \(a_{83}=-0.568707500\) \(a_{84}=+0.000000000\) \(a_{85}=+0.131560795\)
\(a_{86}=-0.076182608\) \(a_{87}=+0.000000000\) \(a_{88}=-0.460117128\) \(a_{89}=-0.467451000\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.139790361\) \(a_{92}=+0.736707846\) \(a_{93}=+0.000000000\) \(a_{94}=+0.075900805\) \(a_{95}=-0.686923911\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.857070029\) \(a_{98}=-1.352606911\) \(a_{99}=+0.000000000\) \(a_{100}=-0.142495215\)

Showing 100 of 180 available coefficients

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