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: \( 4.02981218826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.085163689\) \(a_{3}=+0.999803749\) \(a_{4}=+0.177580233\) \(a_{5}=+1.068730471\)
\(a_{6}=+1.084950725\) \(a_{7}=+1.276299683\) \(a_{8}=-0.892460069\) \(a_{9}=-0.000392463\) \(a_{10}=+1.159747501\)
\(a_{11}=-0.882687079\) \(a_{12}=+0.177545382\) \(a_{13}=-1.202532495\) \(a_{14}=+1.384994072\) \(a_{15}=+1.068520732\)
\(a_{16}=-1.146045494\) \(a_{17}=+0.983124042\) \(a_{18}=-0.000425886\) \(a_{19}=+0.229415734\) \(a_{20}=+0.189785406\)
\(a_{21}=+1.276049208\) \(a_{22}=-0.957859967\) \(a_{23}=-0.795994725\) \(a_{24}=-0.892284923\) \(a_{25}=+0.142184819\)
\(a_{26}=-1.304944598\) \(a_{27}=-1.000196135\) \(a_{28}=+0.226645595\) \(a_{29}=+1.278886763\) \(a_{30}=+1.159519900\)
\(a_{31}=+0.514660202\) \(a_{32}=-0.351186887\) \(a_{33}=-0.882513851\) \(a_{34}=+1.066850513\) \(a_{35}=+1.364020361\)
\(a_{36}=-0.000069694\) \(a_{37}=+0.377405361\) \(a_{38}=+0.248953624\) \(a_{39}=-1.202296497\) \(a_{40}=-0.953799270\)
\(a_{41}=-0.965145774\) \(a_{42}=+1.384722267\) \(a_{43}=-0.698062491\) \(a_{44}=-0.156747777\) \(a_{45}=-0.000419437\)
\(a_{46}=-0.863784572\) \(a_{47}=+0.688295393\) \(a_{48}=-1.145820582\) \(a_{49}=+0.628940880\) \(a_{50}=+0.154293803\)
\(a_{51}=+0.982931104\) \(a_{52}=-0.213546000\) \(a_{53}=+1.921575385\) \(a_{54}=-1.085376528\) \(a_{55}=-0.943354578\)
\(a_{56}=-1.139046503\) \(a_{57}=+0.229370711\) \(a_{58}=+1.387801478\) \(a_{59}=-1.422733133\) \(a_{60}=+0.189748160\)
\(a_{61}=+0.309185150\) \(a_{62}=+0.558490564\) \(a_{63}=-0.000500900\) \(a_{64}=+0.764950236\) \(a_{65}=-1.285183119\)
\(a_{66}=-0.957671987\) \(a_{67}=+1.619587996\) \(a_{68}=+0.174583396\) \(a_{69}=-0.795838510\) \(a_{70}=+1.480185367\)
\(a_{71}=+1.372868255\) \(a_{72}=+0.000350257\) \(a_{73}=+0.099869327\) \(a_{74}=+0.409546594\) \(a_{75}=+0.142156916\)
\(a_{76}=+0.040739699\) \(a_{77}=-1.126573239\) \(a_{78}=-1.304688502\) \(a_{79}=-0.703150889\) \(a_{80}=-1.224813740\)
\(a_{81}=-0.999607383\) \(a_{82}=-1.047341149\) \(a_{83}=+1.120542029\) \(a_{84}=+0.226601115\) \(a_{85}=+1.050694621\)
\(a_{86}=-0.757512068\) \(a_{87}=+1.278635781\) \(a_{88}=+0.787762971\) \(a_{89}=-0.599015758\) \(a_{90}=-0.000455157\)
\(a_{91}=-1.534791841\) \(a_{92}=-0.141352928\) \(a_{93}=+0.514559200\) \(a_{94}=+0.746913168\) \(a_{95}=+0.245183585\)
\(a_{96}=-0.351117966\) \(a_{97}=-0.213244012\) \(a_{98}=+0.682503806\) \(a_{99}=+0.000346422\) \(a_{100}=+0.025249213\)

Showing 100 of 546 available coefficients

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