Properties

Level $839$
Weight $0$
Character 839.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 839 \)
Weight: \( 0 \)
Character: 839.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.139451876 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.258477386\) \(a_{3}=-1.840866181\) \(a_{4}=-0.933189489\) \(a_{5}=-0.805812359\)
\(a_{6}=+0.475822113\) \(a_{7}=-0.493279008\) \(a_{8}=+0.499685669\) \(a_{9}=+2.388788226\) \(a_{10}=+0.208284344\)
\(a_{11}=+0.488183540\) \(a_{12}=+1.717876898\) \(a_{13}=+0.612002854\) \(a_{14}=+0.127501420\) \(a_{15}=+1.483392770\)
\(a_{16}=+0.804032033\) \(a_{17}=+0.157104921\) \(a_{18}=-0.617447500\) \(a_{19}=+0.633093614\) \(a_{20}=+0.751975730\)
\(a_{21}=+0.908060478\) \(a_{22}=-0.126184408\) \(a_{23}=-0.035512995\) \(a_{24}=-0.919854321\) \(a_{25}=-0.350666409\)
\(a_{26}=-0.158188837\) \(a_{27}=-2.556572977\) \(a_{28}=+0.460322832\) \(a_{29}=-1.897755780\) \(a_{30}=-0.383423385\)
\(a_{31}=-0.721842155\) \(a_{32}=-0.707509785\) \(a_{33}=-0.898680728\) \(a_{34}=-0.040608036\) \(a_{35}=+0.397490298\)
\(a_{36}=-2.229191871\) \(a_{37}=+1.753768107\) \(a_{38}=-0.163640373\) \(a_{39}=-1.126615080\) \(a_{40}=-0.402652861\)
\(a_{41}=+1.162992503\) \(a_{42}=-0.234713039\) \(a_{43}=+1.150063455\) \(a_{44}=-0.455567755\) \(a_{45}=-1.924915209\)
\(a_{46}=+0.009179416\) \(a_{47}=+0.626002812\) \(a_{48}=-1.480115500\) \(a_{49}=-0.756675946\) \(a_{50}=+0.090639214\)
\(a_{51}=-0.289208899\) \(a_{52}=-0.571114663\) \(a_{53}=+0.537320647\) \(a_{54}=+0.660816020\) \(a_{55}=-0.393384311\)
\(a_{56}=-0.246484214\) \(a_{57}=-1.165440575\) \(a_{58}=+0.490526735\) \(a_{59}=-0.588063428\) \(a_{60}=-1.384286542\)
\(a_{61}=-0.739844587\) \(a_{62}=+0.186579814\) \(a_{63}=-1.178338982\) \(a_{64}=-0.621156897\) \(a_{65}=-0.493159583\)
\(a_{66}=+0.232288633\) \(a_{67}=+1.358670248\) \(a_{68}=-0.146608660\) \(a_{69}=+0.065374713\) \(a_{70}=-0.102742272\)
\(a_{71}=-1.118756316\) \(a_{72}=+1.193643203\) \(a_{73}=+0.561320584\) \(a_{74}=-0.453309269\) \(a_{75}=+0.645529927\)
\(a_{76}=-0.590796333\) \(a_{77}=-0.240810831\) \(a_{78}=+0.291204469\) \(a_{79}=+0.316151964\) \(a_{80}=-0.647898841\)
\(a_{81}=+2.317520673\) \(a_{82}=-0.300607160\) \(a_{83}=-0.462883162\) \(a_{84}=-0.847392552\) \(a_{85}=-0.126597053\)
\(a_{86}=-0.297265335\) \(a_{87}=+3.493514415\) \(a_{88}=+0.243938430\) \(a_{89}=-1.052722929\) \(a_{90}=+0.497546932\)
\(a_{91}=-0.301887906\) \(a_{92}=+0.033140397\) \(a_{93}=+1.328814635\) \(a_{94}=-0.161807460\) \(a_{95}=-0.510154766\)
\(a_{96}=+1.302430589\) \(a_{97}=-1.205074676\) \(a_{98}=+0.195583493\) \(a_{99}=+1.166167072\) \(a_{100}=+0.327238091\)

Showing 100 of 2142 available coefficients

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