Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 23.5369697073 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.781957075\) \(a_{3}=+0.577350269\) \(a_{4}=+2.175371018\) \(a_{5}=+0.497552113\)
\(a_{6}=+1.028813397\) \(a_{7}=-1.181669356\) \(a_{8}=+2.094460701\) \(a_{9}=+0.333333333\) \(a_{10}=+0.886616509\)
\(a_{11}=+1.765443772\) \(a_{12}=+1.255951043\) \(a_{13}=+0.479066404\) \(a_{14}=-2.105684069\) \(a_{15}=+0.287261847\)
\(a_{16}=+1.556868047\) \(a_{17}=+0.135026866\) \(a_{18}=+0.593985692\) \(a_{19}=+1.531453192\) \(a_{20}=+1.082360447\)
\(a_{21}=-0.682237121\) \(a_{22}=+3.145945021\) \(a_{23}=-0.479120241\) \(a_{24}=+1.209237450\) \(a_{25}=-0.752441895\)
\(a_{26}=+0.853675767\) \(a_{27}=+0.192450090\) \(a_{28}=-2.570569269\) \(a_{29}=+0.363876146\) \(a_{30}=+0.511888280\)
\(a_{31}=-1.154412633\) \(a_{32}=+0.679811331\) \(a_{33}=+1.019279437\) \(a_{34}=+0.240612079\) \(a_{35}=-0.587942085\)
\(a_{36}=+0.725123673\) \(a_{37}=+0.377694402\) \(a_{38}=+2.728983850\) \(a_{39}=+0.276589117\) \(a_{40}=+1.042103348\)
\(a_{41}=-0.766514269\) \(a_{42}=-1.215717264\) \(a_{43}=+0.122481487\) \(a_{44}=+3.840495216\) \(a_{45}=+0.165850704\)
\(a_{46}=-0.853771704\) \(a_{47}=-0.602108733\) \(a_{48}=+0.898858186\) \(a_{49}=+0.396342466\) \(a_{50}=-1.340819158\)
\(a_{51}=+0.077957798\) \(a_{52}=+1.042147170\) \(a_{53}=+0.215640808\) \(a_{54}=+0.342937799\) \(a_{55}=+0.878400280\)
\(a_{56}=-2.474960027\) \(a_{57}=+0.884184912\) \(a_{58}=+0.648411672\) \(a_{59}=-1.020153364\) \(a_{60}=+0.624901096\)
\(a_{61}=+1.700893283\) \(a_{62}=-2.057113758\) \(a_{63}=-0.393889785\) \(a_{64}=-0.345473437\) \(a_{65}=+0.238360502\)
\(a_{66}=+1.816312205\) \(a_{67}=+0.017917925\) \(a_{68}=+0.293733531\) \(a_{69}=-0.276620200\) \(a_{70}=-1.047687558\)
\(a_{71}=-0.904517473\) \(a_{72}=+0.698153567\) \(a_{73}=-1.088982178\) \(a_{74}=+0.673035212\) \(a_{75}=-0.434422530\)
\(a_{76}=+3.331478888\) \(a_{77}=-2.086170805\) \(a_{78}=+0.492869934\) \(a_{79}=-0.313180942\) \(a_{80}=+0.774622987\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.365895524\) \(a_{83}=-0.043181415\) \(a_{84}=-1.484118859\) \(a_{85}=+0.067182903\)
\(a_{86}=+0.218256752\) \(a_{87}=+0.210083991\) \(a_{88}=+3.697652601\) \(a_{89}=-1.046880643\) \(a_{90}=+0.295538836\)
\(a_{91}=-0.566098088\) \(a_{92}=-1.042264287\) \(a_{93}=-0.666500444\) \(a_{94}=-1.072931916\) \(a_{95}=+0.761977772\)
\(a_{96}=+0.392489255\) \(a_{97}=+0.506395539\) \(a_{98}=+0.706265261\) \(a_{99}=+0.588481257\) \(a_{100}=-1.636840290\)

Showing 100 of 1228 available coefficients

Rows: Cols: