Properties

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

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.59237977171 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.396862041\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.212459965\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.280623840\)
\(a_{11}=+0.479890120\) \(a_{12}=+0.288675135\) \(a_{13}=-1.273167866\) \(a_{14}=-0.150231882\) \(a_{15}=-0.229128405\)
\(a_{16}=+0.249999999\) \(a_{17}=+0.170553153\) \(a_{18}=-0.235702248\) \(a_{19}=+1.605197612\) \(a_{20}=-0.198431020\)
\(a_{21}=+0.122663818\) \(a_{22}=-0.339333558\) \(a_{23}=-1.084630015\) \(a_{24}=-0.204124145\) \(a_{25}=-0.842500521\)
\(a_{26}=+0.900265632\) \(a_{27}=+0.192450090\) \(a_{28}=+0.106229982\) \(a_{29}=+0.867862699\) \(a_{30}=+0.162018250\)
\(a_{31}=-0.463261863\) \(a_{32}=-0.176776695\) \(a_{33}=+0.277064690\) \(a_{34}=-0.120599293\) \(a_{35}=-0.084317295\)
\(a_{36}=+0.166666666\) \(a_{37}=+0.466262096\) \(a_{38}=-1.135046128\) \(a_{39}=-0.735063810\) \(a_{40}=+0.140311920\)
\(a_{41}=+0.024554879\) \(a_{42}=-0.086736416\) \(a_{43}=+0.653093276\) \(a_{44}=+0.239945089\) \(a_{45}=-0.132287349\)
\(a_{46}=+0.766949276\) \(a_{47}=+0.736838606\) \(a_{48}=+0.144337549\) \(a_{49}=-0.954860896\) \(a_{50}=+0.595737503\)
\(a_{51}=+0.098469128\) \(a_{52}=-0.636582309\) \(a_{53}=-1.519607387\) \(a_{54}=-0.136083519\) \(a_{55}=-0.190458453\)
\(a_{56}=-0.075127832\) \(a_{57}=+0.926750575\) \(a_{58}=-0.613709724\) \(a_{59}=+0.673323930\) \(a_{60}=-0.114543943\)
\(a_{61}=+0.611312636\) \(a_{62}=+0.327462445\) \(a_{63}=+0.070819987\) \(a_{64}=+0.124999998\) \(a_{65}=+0.505271989\)
\(a_{66}=-0.195914317\) \(a_{67}=+0.112653027\) \(a_{68}=+0.085276579\) \(a_{69}=-0.626211410\) \(a_{70}=+0.059621329\)
\(a_{71}=-1.239519081\) \(a_{72}=-0.117851151\) \(a_{73}=+0.217995742\) \(a_{74}=-0.329697088\) \(a_{75}=-0.486417630\)
\(a_{76}=+0.802598784\) \(a_{77}=+0.101957313\) \(a_{78}=+0.519768658\) \(a_{79}=-0.218689303\) \(a_{80}=-0.099215275\)
\(a_{81}=+0.111114192\) \(a_{82}=-0.017364029\) \(a_{83}=+0.304014343\) \(a_{84}=+0.061331476\) \(a_{85}=-0.067685592\)
\(a_{86}=-0.461813466\) \(a_{87}=+0.501045126\) \(a_{88}=-0.169658614\) \(a_{89}=+1.839886786\) \(a_{90}=+0.093552283\)
\(a_{91}=-0.270533873\) \(a_{92}=-0.542329466\) \(a_{93}=-0.267509905\) \(a_{94}=-0.521007929\) \(a_{95}=-0.637202604\)
\(a_{96}=-0.101737272\) \(a_{97}=-1.479020017\) \(a_{98}=+0.675157471\) \(a_{99}=+0.158705559\) \(a_{100}=-0.420601900\)

Showing 100 of 1000 available coefficients

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