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: \( 2.60729087614 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.182151976\) \(a_{4}=+0.500000000\) \(a_{5}=+0.043473007\)
\(a_{6}=-0.835907679\) \(a_{7}=-1.803526622\) \(a_{8}=-0.353553391\) \(a_{9}=+0.397483295\) \(a_{10}=-0.030740058\)
\(a_{11}=-1.707269672\) \(a_{12}=+0.591075988\) \(a_{13}=-0.116595127\) \(a_{14}=+1.275285905\) \(a_{15}=+0.051391701\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.760223945\) \(a_{18}=-0.281063133\) \(a_{19}=-0.348220555\) \(a_{20}=+0.021736503\)
\(a_{21}=-2.132042560\) \(a_{22}=+1.207221963\) \(a_{23}=-0.784707007\) \(a_{24}=-0.417953839\) \(a_{25}=-0.998110098\)
\(a_{26}=+0.082445205\) \(a_{27}=-0.712266314\) \(a_{28}=-0.901763311\) \(a_{29}=+0.804538689\) \(a_{30}=-0.036339420\)
\(a_{31}=+1.726309142\) \(a_{32}=-0.176776695\) \(a_{33}=-2.018252217\) \(a_{34}=-1.244666288\) \(a_{35}=-0.078404725\)
\(a_{36}=+0.198741647\) \(a_{37}=-0.252069596\) \(a_{38}=+0.246229116\) \(a_{39}=-0.137833160\) \(a_{40}=-0.015370029\)
\(a_{41}=-0.877112413\) \(a_{42}=+1.507581752\) \(a_{43}=+0.152498570\) \(a_{44}=-0.853634836\) \(a_{45}=+0.017279794\)
\(a_{46}=+0.554871646\) \(a_{47}=-0.383822968\) \(a_{48}=+0.295537994\) \(a_{49}=+2.252708277\) \(a_{50}=+0.705770418\)
\(a_{51}=+2.080852215\) \(a_{52}=-0.058297564\) \(a_{53}=-0.804675769\) \(a_{54}=+0.503648341\) \(a_{55}=-0.074220146\)
\(a_{56}=+0.637642952\) \(a_{57}=-0.411649617\) \(a_{58}=-0.568894763\) \(a_{59}=-1.482200674\) \(a_{60}=+0.025695850\)
\(a_{61}=+0.638596437\) \(a_{62}=-1.220684901\) \(a_{63}=-0.716871704\) \(a_{64}=+0.125000000\) \(a_{65}=-0.005068740\)
\(a_{66}=+1.427119828\) \(a_{67}=-0.061215624\) \(a_{68}=+0.880111973\) \(a_{69}=-0.927642939\) \(a_{70}=+0.055440513\)
\(a_{71}=-0.588599848\) \(a_{72}=-0.140531566\) \(a_{73}=-0.282351379\) \(a_{74}=+0.178240120\) \(a_{75}=-1.179917825\)
\(a_{76}=-0.174110278\) \(a_{77}=+3.079106306\) \(a_{78}=+0.097462762\) \(a_{79}=-1.161021678\) \(a_{80}=+0.010868252\)
\(a_{81}=-1.239490324\) \(a_{82}=+0.620212135\) \(a_{83}=-1.256326894\) \(a_{84}=-1.066021280\) \(a_{85}=+0.076522229\)
\(a_{86}=-0.107832773\) \(a_{87}=+0.951086999\) \(a_{88}=+0.603610981\) \(a_{89}=-0.537890813\) \(a_{90}=-0.012218660\)
\(a_{91}=+0.210282415\) \(a_{92}=-0.392353504\) \(a_{93}=+2.040759765\) \(a_{94}=+0.271403823\) \(a_{95}=-0.015138195\)
\(a_{96}=-0.208976920\) \(a_{97}=-0.079796595\) \(a_{98}=-1.592905299\) \(a_{99}=-0.678611174\) \(a_{100}=-0.499055049\)

Showing 100 of 562 available coefficients

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