Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.77688712054 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.786030064\) \(a_{3}=-1.345539141\) \(a_{4}=+2.189903392\) \(a_{5}=-1.562156074\)
\(a_{6}=+2.403173360\) \(a_{7}=-0.695748741\) \(a_{8}=-2.125203233\) \(a_{9}=+0.810475581\) \(a_{10}=+2.790057717\)
\(a_{11}=-0.406103474\) \(a_{12}=-2.946600731\) \(a_{13}=-0.031894160\) \(a_{14}=+1.242628170\) \(a_{15}=+2.101942146\)
\(a_{16}=+1.605773477\) \(a_{17}=-0.693063477\) \(a_{18}=-1.447533755\) \(a_{19}=+0.229415734\) \(a_{20}=-3.420970892\)
\(a_{21}=+0.936157165\) \(a_{22}=+0.725313015\) \(a_{23}=-1.628035048\) \(a_{24}=+2.859544135\) \(a_{25}=+1.440331610\)
\(a_{26}=+0.056963930\) \(a_{27}=+0.255012521\) \(a_{28}=-1.523622530\) \(a_{29}=+0.625565219\) \(a_{30}=-3.754131868\)
\(a_{31}=+0.416112877\) \(a_{32}=-0.742756477\) \(a_{33}=+0.546428119\) \(a_{34}=+1.237832208\) \(a_{35}=+1.086868125\)
\(a_{36}=+1.774863239\) \(a_{37}=-0.903048194\) \(a_{38}=-0.409743415\) \(a_{39}=+0.042914873\) \(a_{40}=+3.319899155\)
\(a_{41}=-0.901164256\) \(a_{42}=-1.672004898\) \(a_{43}=-0.219908540\) \(a_{44}=-0.889327379\) \(a_{45}=-1.266089353\)
\(a_{46}=+2.907719548\) \(a_{47}=+0.444624001\) \(a_{48}=-2.160631080\) \(a_{49}=-0.515933687\) \(a_{50}=-2.572475539\)
\(a_{51}=+0.932544034\) \(a_{52}=-0.069845149\) \(a_{53}=-0.799554616\) \(a_{54}=-0.455460017\) \(a_{55}=+0.634396987\)
\(a_{56}=+1.478607461\) \(a_{57}=-0.308687786\) \(a_{58}=-1.117278267\) \(a_{59}=+1.593249276\) \(a_{60}=+4.603050209\)
\(a_{61}=-0.231616289\) \(a_{62}=-0.743190088\) \(a_{63}=-0.563887312\) \(a_{64}=-0.279188058\) \(a_{65}=+0.049823585\)
\(a_{66}=-0.975937059\) \(a_{67}=+1.759344145\) \(a_{68}=-1.517742088\) \(a_{69}=+2.190584865\) \(a_{70}=-1.941179083\)
\(a_{71}=+0.444842001\) \(a_{72}=-1.722425348\) \(a_{73}=-0.265831721\) \(a_{74}=+1.612871205\) \(a_{75}=-1.938022557\)
\(a_{76}=+0.502398285\) \(a_{77}=+0.282545996\) \(a_{78}=-0.076647196\) \(a_{79}=-1.797473614\) \(a_{80}=-2.508468754\)
\(a_{81}=-1.153604862\) \(a_{82}=+1.609506400\) \(a_{83}=+1.297669245\) \(a_{84}=+2.050093739\) \(a_{85}=+1.082673349\)
\(a_{86}=+0.392763293\) \(a_{87}=-0.841722430\) \(a_{88}=+0.863052390\) \(a_{89}=-0.044766094\) \(a_{90}=+2.261273691\)
\(a_{91}=+0.022190325\) \(a_{92}=-3.565239544\) \(a_{93}=-0.559896034\) \(a_{94}=-0.794111769\) \(a_{95}=-0.358383277\)
\(a_{96}=+0.999407838\) \(a_{97}=-1.136220647\) \(a_{98}=+0.921473101\) \(a_{99}=-0.329136995\) \(a_{100}=+3.154187030\)

Showing 100 of 1500 available coefficients

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