Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 15.95460255 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.398415477\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.735176001\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.988829067\)
\(a_{11}=-1.405181543\) \(a_{12}=+0.288675135\) \(a_{13}=-0.722142154\) \(a_{14}=+0.519847935\) \(a_{15}=+0.807375552\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.303099610\) \(a_{18}=-0.235702260\) \(a_{19}=+1.451603919\) \(a_{20}=+0.699207739\)
\(a_{21}=-0.424454062\) \(a_{22}=+0.993613398\) \(a_{23}=-0.038140642\) \(a_{24}=-0.204124145\) \(a_{25}=+0.955565847\)
\(a_{26}=+0.510631614\) \(a_{27}=+0.192450090\) \(a_{28}=-0.367588000\) \(a_{29}=-0.312370563\) \(a_{30}=-0.570900728\)
\(a_{31}=-1.794953984\) \(a_{32}=-0.176776695\) \(a_{33}=-0.811281942\) \(a_{34}=+0.921430571\) \(a_{35}=-1.028081498\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.555107160\) \(a_{38}=-1.026438974\) \(a_{39}=-0.416928967\) \(a_{40}=-0.494414533\)
\(a_{41}=-0.172863878\) \(a_{42}=+0.300134345\) \(a_{43}=-0.996147570\) \(a_{44}=-0.702590771\) \(a_{45}=+0.466138492\)
\(a_{46}=+0.026969506\) \(a_{47}=+1.033109206\) \(a_{48}=+0.144337567\) \(a_{49}=-0.459516248\) \(a_{50}=-0.675687090\)
\(a_{51}=-0.752344910\) \(a_{52}=-0.361071077\) \(a_{53}=+1.791913841\) \(a_{54}=-0.136082763\) \(a_{55}=-1.965027617\)
\(a_{56}=+0.259923968\) \(a_{57}=+0.838083913\) \(a_{58}=+0.220879344\) \(a_{59}=-0.931266863\) \(a_{60}=+0.403687776\)
\(a_{61}=+0.020559637\) \(a_{62}=+1.269224134\) \(a_{63}=-0.245058667\) \(a_{64}=+0.125000000\) \(a_{65}=-1.009854765\)
\(a_{66}=+0.573662963\) \(a_{67}=+0.057472500\) \(a_{68}=-0.651549805\) \(a_{69}=-0.022020510\) \(a_{70}=+0.726963399\)
\(a_{71}=-1.395262900\) \(a_{72}=-0.117851130\) \(a_{73}=-0.825125000\) \(a_{74}=+0.392520037\) \(a_{75}=+0.551696199\)
\(a_{76}=+0.725801959\) \(a_{77}=+1.033055747\) \(a_{78}=+0.294813300\) \(a_{79}=-0.082153000\) \(a_{80}=+0.349603869\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.122233221\) \(a_{83}=-1.723700047\) \(a_{84}=-0.212227031\) \(a_{85}=-1.822274662\)
\(a_{86}=+0.704382702\) \(a_{87}=-0.180347229\) \(a_{88}=+0.496806699\) \(a_{89}=+1.181480050\) \(a_{90}=-0.329609689\)
\(a_{91}=+0.530901581\) \(a_{92}=-0.019070321\) \(a_{93}=-1.036317166\) \(a_{94}=-0.730518525\) \(a_{95}=+2.029945386\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.225999832\) \(a_{98}=+0.324927055\) \(a_{99}=-0.468393848\) \(a_{100}=+0.477782923\)

Showing 100 of 108 available coefficients

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