Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 30.8564751304 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.172728407\) \(a_{3}=-0.577350269\) \(a_{4}=+0.375291916\) \(a_{5}=-1.429471324\)
\(a_{6}=+0.677075061\) \(a_{7}=+1.234602812\) \(a_{8}=+0.732612916\) \(a_{9}=+0.333333333\) \(a_{10}=+1.676381628\)
\(a_{11}=+1.168404077\) \(a_{12}=-0.216674889\) \(a_{13}=-0.610893031\) \(a_{14}=-1.447853789\) \(a_{15}=+0.825305654\)
\(a_{16}=-1.234447894\) \(a_{17}=+0.897404106\) \(a_{18}=-0.390909469\) \(a_{19}=+1.713478301\) \(a_{20}=-0.536469032\)
\(a_{21}=-0.712798266\) \(a_{22}=-1.370220651\) \(a_{23}=-0.155844987\) \(a_{24}=-0.422974264\) \(a_{25}=+1.043388265\)
\(a_{26}=+0.716411610\) \(a_{27}=-0.192450090\) \(a_{28}=+0.463336455\) \(a_{29}=-1.211697679\) \(a_{30}=-0.967859384\)
\(a_{31}=-0.134775206\) \(a_{32}=+0.715059195\) \(a_{33}=-0.674578408\) \(a_{34}=-1.052411288\) \(a_{35}=-1.764829316\)
\(a_{36}=+0.125097305\) \(a_{37}=+0.416719091\) \(a_{38}=-2.009444678\) \(a_{39}=+0.352699256\) \(a_{40}=-1.047249155\)
\(a_{41}=-0.605862914\) \(a_{42}=+0.835918775\) \(a_{43}=+1.563069109\) \(a_{44}=+0.438492604\) \(a_{45}=-0.476490441\)
\(a_{46}=+0.182763843\) \(a_{47}=-1.199132047\) \(a_{48}=+0.712708824\) \(a_{49}=+0.524244104\) \(a_{50}=-1.223611058\)
\(a_{51}=-0.518116502\) \(a_{52}=-0.229263216\) \(a_{53}=-0.532309635\) \(a_{54}=+0.225691687\) \(a_{55}=-1.670200122\)
\(a_{56}=+0.904485967\) \(a_{57}=-0.989277159\) \(a_{58}=+1.420992288\) \(a_{59}=-0.193076786\) \(a_{60}=+0.309730540\)
\(a_{61}=+1.182413862\) \(a_{62}=+0.158054712\) \(a_{63}=+0.411534271\) \(a_{64}=+0.395877663\) \(a_{65}=+0.873254069\)
\(a_{66}=+0.791097262\) \(a_{67}=+0.061621761\) \(a_{68}=+0.336788506\) \(a_{69}=+0.089977145\) \(a_{70}=+2.069665472\)
\(a_{71}=+1.120451748\) \(a_{72}=+0.244204305\) \(a_{73}=-0.089973154\) \(a_{74}=-0.488698315\) \(a_{75}=-0.602400496\)
\(a_{76}=+0.643054555\) \(a_{77}=+1.442514959\) \(a_{78}=-0.413620436\) \(a_{79}=-0.641858926\) \(a_{80}=+1.764607865\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.710512649\) \(a_{83}=+0.319138744\) \(a_{84}=-0.267507427\) \(a_{85}=-1.282813436\)
\(a_{86}=-1.833055545\) \(a_{87}=+0.699573981\) \(a_{88}=+0.855987918\) \(a_{89}=+1.446089596\) \(a_{90}=+0.558793876\)
\(a_{91}=-0.754210253\) \(a_{92}=-0.058487364\) \(a_{93}=+0.077812501\) \(a_{94}=+1.406256215\) \(a_{95}=-2.449368096\)
\(a_{96}=-0.412839619\) \(a_{97}=+1.298587510\) \(a_{98}=-0.614795953\) \(a_{99}=+0.389468026\) \(a_{100}=+0.391575181\)

Showing 100 of 1228 available coefficients

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