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: \( 4.39865050004 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+0.845582386\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.706714691\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.597917039\)
\(a_{11}=-1.301407767\) \(a_{12}=+0.000000000\) \(a_{13}=+0.081906110\) \(a_{14}=+1.206829532\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.155586017\) \(a_{18}=+0.000000000\) \(a_{19}=+0.812367811\) \(a_{20}=+0.422791193\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.920234257\) \(a_{23}=-1.473415692\) \(a_{24}=+0.000000000\) \(a_{25}=-0.284990429\)
\(a_{26}=+0.057916366\) \(a_{27}=+0.000000000\) \(a_{28}=+0.853357346\) \(a_{29}=-0.045378970\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.018859736\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.110015928\) \(a_{35}=+1.443167880\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.770076818\) \(a_{38}=+0.574430788\) \(a_{39}=+0.000000000\) \(a_{40}=+0.298958519\)
\(a_{41}=-1.374924163\) \(a_{42}=+0.000000000\) \(a_{43}=+0.107738477\) \(a_{44}=-0.650703883\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.041862228\) \(a_{47}=+0.107339948\) \(a_{48}=+0.000000000\) \(a_{49}=+1.912875037\) \(a_{50}=-0.201518665\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.040953055\) \(a_{53}=-0.972747865\) \(a_{54}=+0.000000000\) \(a_{55}=-1.100447484\)
\(a_{56}=+0.603414766\) \(a_{57}=+0.000000000\) \(a_{58}=-0.032087778\) \(a_{59}=+1.764962531\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.487287470\) \(a_{62}=+0.013335847\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+0.069258364\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.619053917\) \(a_{68}=+0.077793008\) \(a_{69}=+0.000000000\) \(a_{70}=+1.020473794\)
\(a_{71}=+0.161407862\) \(a_{72}=+0.000000000\) \(a_{73}=-1.336952463\) \(a_{74}=-0.544526540\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.406183905\) \(a_{77}=-2.221131755\) \(a_{78}=+0.000000000\) \(a_{79}=+0.526593170\) \(a_{80}=+0.211395596\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.972218199\) \(a_{83}=+0.568707470\) \(a_{84}=+0.000000000\) \(a_{85}=+0.131560795\)
\(a_{86}=+0.076182608\) \(a_{87}=+0.000000000\) \(a_{88}=-0.460117128\) \(a_{89}=+0.467451471\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.139790361\) \(a_{92}=-0.736707846\) \(a_{93}=+0.000000000\) \(a_{94}=+0.075900805\) \(a_{95}=+0.686923911\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.857070800\) \(a_{98}=+1.352606911\) \(a_{99}=+0.000000000\) \(a_{100}=-0.142495215\)

Showing 100 of 198 available coefficients

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