Properties

Level $62$
Weight $0$
Character 62.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 62 = 2 \cdot 31 \)
Weight: \( 0 \)
Character: 62.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.730579785457 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.105442598\) \(a_{4}=+0.500000000\) \(a_{5}=-1.050900268\)
\(a_{6}=+0.781665957\) \(a_{7}=-1.388296649\) \(a_{8}=-0.353553391\) \(a_{9}=+0.222003336\) \(a_{10}=+0.743098706\)
\(a_{11}=+1.337106039\) \(a_{12}=-0.552721299\) \(a_{13}=+0.221326150\) \(a_{14}=+0.981673975\) \(a_{15}=+1.161709923\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.473694399\) \(a_{18}=-0.156980065\) \(a_{19}=-0.794945696\) \(a_{20}=-0.525450134\)
\(a_{21}=+1.534682253\) \(a_{22}=-0.945476748\) \(a_{23}=-0.580163993\) \(a_{24}=+0.390832978\) \(a_{25}=+0.104391374\)
\(a_{26}=-0.156501221\) \(a_{27}=+0.860030653\) \(a_{28}=-0.694148324\) \(a_{29}=-1.280479804\) \(a_{30}=-0.821452964\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.176776695\) \(a_{33}=-1.478093973\) \(a_{34}=+0.334952522\) \(a_{35}=+1.458961321\)
\(a_{36}=+0.111001668\) \(a_{37}=+0.512204574\) \(a_{38}=+0.562111492\) \(a_{39}=-0.244663354\) \(a_{40}=+0.371549353\)
\(a_{41}=-0.286941424\) \(a_{42}=-1.085184228\) \(a_{43}=-0.513323813\) \(a_{44}=+0.668553020\) \(a_{45}=-0.233303366\)
\(a_{46}=+0.410237894\) \(a_{47}=-1.192975363\) \(a_{48}=-0.276360649\) \(a_{49}=+0.927367585\) \(a_{50}=-0.073815849\)
\(a_{51}=+0.523641967\) \(a_{52}=+0.110663075\) \(a_{53}=+0.887446935\) \(a_{54}=-0.608133507\) \(a_{55}=-1.405165096\)
\(a_{56}=+0.490836987\) \(a_{57}=+0.878766835\) \(a_{58}=+0.905435952\) \(a_{59}=+1.384311575\) \(a_{60}=+0.580854961\)
\(a_{61}=+0.212839082\) \(a_{62}=+0.127000127\) \(a_{63}=-0.308206488\) \(a_{64}=+0.125000000\) \(a_{65}=-0.232591710\)
\(a_{66}=+1.045170272\) \(a_{67}=+0.982937578\) \(a_{68}=-0.236847199\) \(a_{69}=+0.641337992\) \(a_{70}=-1.031641443\)
\(a_{71}=-0.683396608\) \(a_{72}=-0.078490032\) \(a_{73}=-0.344956146\) \(a_{74}=-0.362183327\) \(a_{75}=-0.115398672\)
\(a_{76}=-0.397472848\) \(a_{77}=-1.856299833\) \(a_{78}=+0.173003117\) \(a_{79}=-1.603451795\) \(a_{80}=-0.262725067\)
\(a_{81}=-1.172717855\) \(a_{82}=+0.202898227\) \(a_{83}=-0.868232179\) \(a_{84}=+0.767341127\) \(a_{85}=+0.497805571\)
\(a_{86}=+0.362974749\) \(a_{87}=+1.415496920\) \(a_{88}=-0.472738374\) \(a_{89}=+1.169629415\) \(a_{90}=+0.164970392\)
\(a_{91}=-0.307266352\) \(a_{92}=-0.290081997\) \(a_{93}=+0.198543352\) \(a_{94}=+0.843560969\) \(a_{95}=+0.835408645\)
\(a_{96}=+0.195416489\) \(a_{97}=-0.504266873\) \(a_{98}=-0.655747908\) \(a_{99}=+0.296842002\) \(a_{100}=+0.052195687\)

Showing 100 of 568 available coefficients

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