Properties

Level $86$
Weight $0$
Character 86.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 86 = 2 \cdot 43 \)
Weight: \( 0 \)
Character: 86.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.62370207241 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.072161622\) \(a_{4}=+0.500000000\) \(a_{5}=+1.099903371\)
\(a_{6}=-0.051025972\) \(a_{7}=-0.489147511\) \(a_{8}=+0.353553391\) \(a_{9}=-0.994792700\) \(a_{10}=+0.777749132\)
\(a_{11}=-0.819302361\) \(a_{12}=-0.036080811\) \(a_{13}=+1.048785997\) \(a_{14}=-0.345879522\) \(a_{15}=-0.079370811\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.994004263\) \(a_{18}=-0.703424664\) \(a_{19}=+1.734908367\) \(a_{20}=+0.549951685\)
\(a_{21}=+0.035297678\) \(a_{22}=-0.579334256\) \(a_{23}=-1.036642097\) \(a_{24}=-0.025512986\) \(a_{25}=+0.209787425\)
\(a_{26}=+0.741603690\) \(a_{27}=+0.143947477\) \(a_{28}=-0.244573755\) \(a_{29}=+0.235524889\) \(a_{30}=-0.056123639\)
\(a_{31}=-1.032912161\) \(a_{32}=+0.176776695\) \(a_{33}=+0.059122187\) \(a_{34}=+0.702867155\) \(a_{35}=-0.538014996\)
\(a_{36}=-0.497396350\) \(a_{37}=-0.386143432\) \(a_{38}=+1.226765471\) \(a_{39}=-0.075682099\) \(a_{40}=+0.388874566\)
\(a_{41}=+1.398582557\) \(a_{42}=+0.024959227\) \(a_{43}=+0.152498570\) \(a_{44}=-0.409651181\) \(a_{45}=-1.094175844\)
\(a_{46}=-0.733016656\) \(a_{47}=-0.116758908\) \(a_{48}=-0.018040406\) \(a_{49}=-0.760734713\) \(a_{50}=+0.148342111\)
\(a_{51}=-0.071728960\) \(a_{52}=+0.524392998\) \(a_{53}=-0.034669267\) \(a_{54}=+0.101786237\) \(a_{55}=-0.901153429\)
\(a_{56}=-0.172939761\) \(a_{57}=-0.125193802\) \(a_{58}=+0.166541246\) \(a_{59}=-1.480974283\) \(a_{60}=-0.039685406\)
\(a_{61}=+0.289151816\) \(a_{62}=-0.730379194\) \(a_{63}=+0.486600373\) \(a_{64}=+0.125000000\) \(a_{65}=+1.153563253\)
\(a_{66}=+0.041805700\) \(a_{67}=-1.097701320\) \(a_{68}=+0.497002131\) \(a_{69}=+0.074805775\) \(a_{70}=-0.380434052\)
\(a_{71}=+0.486196516\) \(a_{72}=-0.351712332\) \(a_{73}=+0.399086115\) \(a_{74}=-0.273044639\) \(a_{75}=-0.015138601\)
\(a_{76}=+0.867454183\) \(a_{77}=+0.400759711\) \(a_{78}=-0.053515325\) \(a_{79}=-0.804992812\) \(a_{80}=+0.274975843\)
\(a_{81}=+0.984405217\) \(a_{82}=+0.988947210\) \(a_{83}=-1.270738316\) \(a_{84}=+0.017648839\) \(a_{85}=+1.093308639\)
\(a_{86}=+0.107832773\) \(a_{87}=-0.016995858\) \(a_{88}=-0.289667128\) \(a_{89}=+1.840156661\) \(a_{90}=-0.773699159\)
\(a_{91}=-0.513011060\) \(a_{92}=-0.518321048\) \(a_{93}=+0.074536617\) \(a_{94}=-0.082561016\) \(a_{95}=+1.908231560\)
\(a_{96}=-0.012756493\) \(a_{97}=-1.375513496\) \(a_{98}=-0.537920674\) \(a_{99}=+0.815036008\) \(a_{100}=+0.104893712\)

Showing 100 of 718 available coefficients

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