Properties

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

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Maass form invariants

Level: \( 86 = 2 \cdot 43 \)
Weight: \( 0 \)
Character: 86.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.15309047426 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.918558252\) \(a_{4}=+0.500000000\) \(a_{5}=+1.184251844\)
\(a_{6}=+1.356625550\) \(a_{7}=-0.207437782\) \(a_{8}=-0.353553391\) \(a_{9}=+2.680865768\) \(a_{10}=-0.837392510\)
\(a_{11}=-0.456957832\) \(a_{12}=-0.959279126\) \(a_{13}=-0.383226305\) \(a_{14}=+0.146680662\) \(a_{15}=-2.272056149\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.794628134\) \(a_{18}=-1.895658364\) \(a_{19}=-1.008745675\) \(a_{20}=+0.592125922\)
\(a_{21}=+0.397981469\) \(a_{22}=+0.323117982\) \(a_{23}=+0.907405542\) \(a_{24}=+0.678312775\) \(a_{25}=+0.402452430\)
\(a_{26}=+0.270981919\) \(a_{27}=-3.224838891\) \(a_{28}=-0.103718891\) \(a_{29}=-1.349489335\) \(a_{30}=+1.606586310\)
\(a_{31}=-0.664044058\) \(a_{32}=-0.176776695\) \(a_{33}=+0.876700220\) \(a_{34}=-1.268993723\) \(a_{35}=-0.245658576\)
\(a_{36}=+1.340432884\) \(a_{37}=+0.769856502\) \(a_{38}=+0.713290907\) \(a_{39}=+0.735241991\) \(a_{40}=-0.418696255\)
\(a_{41}=-1.168958730\) \(a_{42}=-0.281415395\) \(a_{43}=-0.152498570\) \(a_{44}=-0.228478916\) \(a_{45}=+3.174820230\)
\(a_{46}=-0.641632612\) \(a_{47}=+1.426711883\) \(a_{48}=-0.479639563\) \(a_{49}=-0.956969567\) \(a_{50}=-0.284576843\)
\(a_{51}=-3.443098615\) \(a_{52}=-0.191613153\) \(a_{53}=-1.375193509\) \(a_{54}=+2.280305448\) \(a_{55}=-0.541153155\)
\(a_{56}=+0.073340331\) \(a_{57}=+1.935337340\) \(a_{58}=+0.954233060\) \(a_{59}=-0.403859171\) \(a_{60}=-1.136028074\)
\(a_{61}=-0.246179909\) \(a_{62}=+0.469550057\) \(a_{63}=-0.556112856\) \(a_{64}=+0.125000000\) \(a_{65}=-0.453836452\)
\(a_{66}=-0.619920671\) \(a_{67}=+0.564508355\) \(a_{68}=+0.897314067\) \(a_{69}=-1.740910387\) \(a_{70}=+0.173706845\)
\(a_{71}=-1.620764349\) \(a_{72}=-0.947829182\) \(a_{73}=-0.049562794\) \(a_{74}=-0.544370753\) \(a_{75}=-0.772128436\)
\(a_{76}=-0.504372837\) \(a_{77}=+0.094790328\) \(a_{78}=-0.519894598\) \(a_{79}=-0.080386245\) \(a_{80}=+0.296062961\)
\(a_{81}=+3.506175517\) \(a_{82}=+0.826578645\) \(a_{83}=-1.330738380\) \(a_{84}=+0.198990734\) \(a_{85}=+2.125291698\)
\(a_{86}=+0.107832773\) \(a_{87}=+2.589073877\) \(a_{88}=+0.161558991\) \(a_{89}=+0.542294101\) \(a_{90}=-2.244936914\)
\(a_{91}=+0.079495588\) \(a_{92}=+0.453702771\) \(a_{93}=+1.274007253\) \(a_{94}=-1.008837648\) \(a_{95}=-1.194608971\)
\(a_{96}=+0.339156388\) \(a_{97}=+0.323476210\) \(a_{98}=+0.676679670\) \(a_{99}=-1.225042642\) \(a_{100}=+0.201226215\)

Showing 100 of 546 available coefficients

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