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: \( 9.37443036553 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.124525626\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.306241333\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.088052915\)
\(a_{11}=+1.748046417\) \(a_{12}=-0.288675135\) \(a_{13}=+1.314614001\) \(a_{14}=+0.216545323\) \(a_{15}=-0.071894904\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.516100551\) \(a_{18}=+0.235702260\) \(a_{19}=+0.940487245\) \(a_{20}=+0.062262813\)
\(a_{21}=-0.176808516\) \(a_{22}=+1.236055475\) \(a_{23}=-1.447929995\) \(a_{24}=-0.204124145\) \(a_{25}=-0.984493368\)
\(a_{26}=+0.929572475\) \(a_{27}=-0.192450090\) \(a_{28}=+0.153120666\) \(a_{29}=+1.721172993\) \(a_{30}=-0.050837374\)
\(a_{31}=-0.760570845\) \(a_{32}=+0.176776695\) \(a_{33}=-1.009235069\) \(a_{34}=-0.364938199\) \(a_{35}=+0.038134894\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.265609915\) \(a_{38}=+0.665024908\) \(a_{39}=-0.758992747\) \(a_{40}=+0.044026457\)
\(a_{41}=+0.635149447\) \(a_{42}=-0.125022501\) \(a_{43}=-0.173835282\) \(a_{44}=+0.874023209\) \(a_{45}=+0.041508542\)
\(a_{46}=-1.023841118\) \(a_{47}=+0.592701202\) \(a_{48}=-0.144337567\) \(a_{49}=-0.906216246\) \(a_{50}=-0.696141937\)
\(a_{51}=+0.297970792\) \(a_{52}=+0.657307000\) \(a_{53}=+0.072342269\) \(a_{54}=-0.136082764\) \(a_{55}=+0.217676575\)
\(a_{56}=+0.108272662\) \(a_{57}=-0.542990564\) \(a_{58}=+1.217053095\) \(a_{59}=+0.707218447\) \(a_{60}=-0.035947452\)
\(a_{61}=-0.612580249\) \(a_{62}=-0.537804802\) \(a_{63}=+0.102080444\) \(a_{64}=+0.125000000\) \(a_{65}=+0.163703133\)
\(a_{66}=-0.713636962\) \(a_{67}=-1.496707840\) \(a_{68}=-0.258050276\) \(a_{69}=+0.835962774\) \(a_{70}=+0.026965446\)
\(a_{71}=+0.278281881\) \(a_{72}=+0.117851128\) \(a_{73}=+0.897949909\) \(a_{74}=+0.187814572\) \(a_{75}=+0.568397511\)
\(a_{76}=+0.470243622\) \(a_{77}=+0.535324064\) \(a_{78}=-0.536688918\) \(a_{79}=-1.461138718\) \(a_{80}=+0.031131407\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.449118481\) \(a_{83}=-1.121966849\) \(a_{84}=-0.088404258\) \(a_{85}=-0.064267744\)
\(a_{86}=-0.122920106\) \(a_{87}=-0.993719691\) \(a_{88}=+0.618027738\) \(a_{89}=+1.033986755\) \(a_{90}=+0.029350972\)
\(a_{91}=+0.402589143\) \(a_{92}=-0.723964998\) \(a_{93}=+0.439115782\) \(a_{94}=+0.419103039\) \(a_{95}=+0.117114764\)
\(a_{96}=-0.102062073\) \(a_{97}=-0.089169069\) \(a_{98}=-0.640791653\) \(a_{99}=+0.582682139\) \(a_{100}=-0.492246684\)

Showing 100 of 1000 available coefficients

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