Properties

Level $82$
Weight $0$
Character 82.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 82 = 2 \cdot 41 \)
Weight: \( 0 \)
Character: 82.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.75871129504 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.392166338\) \(a_{4}=+0.500000000\) \(a_{5}=+0.681277546\)
\(a_{6}=+0.984410258\) \(a_{7}=-1.716943225\) \(a_{8}=+0.353553391\) \(a_{9}=+0.938127112\) \(a_{10}=+0.481735973\)
\(a_{11}=+0.142035831\) \(a_{12}=+0.696083169\) \(a_{13}=+0.718788381\) \(a_{14}=-1.214062197\) \(a_{15}=+0.948451666\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.772422522\) \(a_{18}=+0.663356043\) \(a_{19}=+0.260289551\) \(a_{20}=+0.340638773\)
\(a_{21}=-2.390270561\) \(a_{22}=+0.100434499\) \(a_{23}=+1.450331122\) \(a_{24}=+0.492205129\) \(a_{25}=-0.535860905\)
\(a_{26}=+0.508260138\) \(a_{27}=-0.086137352\) \(a_{28}=-0.858471612\) \(a_{29}=-0.712192878\) \(a_{30}=+0.670656605\)
\(a_{31}=-0.462264906\) \(a_{32}=+0.176776695\) \(a_{33}=+0.197737503\) \(a_{34}=-1.253291984\) \(a_{35}=-1.169714867\)
\(a_{36}=+0.469063556\) \(a_{37}=+0.676207041\) \(a_{38}=+0.184052507\) \(a_{39}=+1.000672988\) \(a_{40}=+0.240867986\)
\(a_{41}=-0.156173762\) \(a_{42}=-1.690176523\) \(a_{43}=+1.279680923\) \(a_{44}=+0.071017916\) \(a_{45}=+0.639124937\)
\(a_{46}=+1.025538971\) \(a_{47}=+1.880595080\) \(a_{48}=+0.348041584\) \(a_{49}=+1.947894036\) \(a_{50}=-0.378910880\)
\(a_{51}=-2.467506971\) \(a_{52}=+0.359394190\) \(a_{53}=-1.145971086\) \(a_{54}=-0.060908306\) \(a_{55}=+0.096765822\)
\(a_{56}=-0.607031099\) \(a_{57}=+0.362366352\) \(a_{58}=-0.503596414\) \(a_{59}=+0.355162325\) \(a_{60}=+0.474225833\)
\(a_{61}=+0.439722264\) \(a_{62}=-0.326870650\) \(a_{63}=-1.610710989\) \(a_{64}=+0.125000000\) \(a_{65}=+0.489694384\)
\(a_{66}=+0.139821529\) \(a_{67}=-0.554350241\) \(a_{68}=-0.886211261\) \(a_{69}=+2.019102166\) \(a_{70}=-0.827113314\)
\(a_{71}=+1.310657732\) \(a_{72}=+0.331678021\) \(a_{73}=-0.172619249\) \(a_{74}=+0.478150584\) \(a_{75}=-0.746007514\)
\(a_{76}=+0.130144776\) \(a_{77}=-0.243867458\) \(a_{78}=+0.707582656\) \(a_{79}=+0.582768373\) \(a_{80}=+0.170319386\)
\(a_{81}=-1.058044634\) \(a_{82}=-0.110431526\) \(a_{83}=-1.112904756\) \(a_{84}=-1.195135281\) \(a_{85}=-1.207511666\)
\(a_{86}=+0.904871059\) \(a_{87}=-0.991490952\) \(a_{88}=+0.050217250\) \(a_{89}=-1.143215675\) \(a_{90}=+0.451929577\)
\(a_{91}=-1.234118841\) \(a_{92}=+0.725165561\) \(a_{93}=-0.643549641\) \(a_{94}=+1.329781534\) \(a_{95}=+0.177329427\)
\(a_{96}=+0.246102565\) \(a_{97}=-0.026709112\) \(a_{98}=+1.377369082\) \(a_{99}=+0.133247664\) \(a_{100}=-0.267930453\)

Showing 100 of 726 available coefficients

Rows: Cols: