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: \( 20.018381712 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.139990668\) \(a_{3}=+0.577350269\) \(a_{4}=-0.980402613\) \(a_{5}=+1.809091619\)
\(a_{6}=+0.080823650\) \(a_{7}=-0.186868779\) \(a_{8}=-0.277237885\) \(a_{9}=+0.333333333\) \(a_{10}=+0.253255945\)
\(a_{11}=+0.660219109\) \(a_{12}=-0.566035712\) \(a_{13}=-0.092202425\) \(a_{14}=-0.026159885\) \(a_{15}=+1.044479533\)
\(a_{16}=+0.941591896\) \(a_{17}=-1.390069150\) \(a_{18}=+0.046663556\) \(a_{19}=+0.725386140\) \(a_{20}=-1.773638150\)
\(a_{21}=-0.107888740\) \(a_{22}=+0.092424514\) \(a_{23}=+0.385973335\) \(a_{24}=-0.160063368\) \(a_{25}=+2.272812486\)
\(a_{26}=-0.012907479\) \(a_{27}=+0.192450090\) \(a_{28}=+0.183206639\) \(a_{29}=+1.688107733\) \(a_{30}=+0.146217388\)
\(a_{31}=+0.683457281\) \(a_{32}=+0.409051964\) \(a_{33}=+0.381177680\) \(a_{34}=-0.194596709\) \(a_{35}=-0.338062742\)
\(a_{36}=-0.326800871\) \(a_{37}=+1.627558859\) \(a_{38}=+0.101547291\) \(a_{39}=-0.053233095\) \(a_{40}=-0.501548735\)
\(a_{41}=+0.218131867\) \(a_{42}=-0.015103417\) \(a_{43}=-0.188542080\) \(a_{44}=-0.647280540\) \(a_{45}=+0.603030540\)
\(a_{46}=+0.054032665\) \(a_{47}=+0.692312237\) \(a_{48}=+0.543628335\) \(a_{49}=-0.965080059\) \(a_{50}=+0.318172539\)
\(a_{51}=-0.802556798\) \(a_{52}=+0.090395498\) \(a_{53}=-0.587516286\) \(a_{54}=+0.026941217\) \(a_{55}=+1.194396857\)
\(a_{56}=+0.051807105\) \(a_{57}=+0.418801883\) \(a_{58}=+0.236319330\) \(a_{59}=-1.011552176\) \(a_{60}=-1.024010463\)
\(a_{61}=+1.193880013\) \(a_{62}=+0.095677642\) \(a_{63}=-0.062289593\) \(a_{64}=-0.884328438\) \(a_{65}=-0.166802634\)
\(a_{66}=+0.053361318\) \(a_{67}=+0.399372457\) \(a_{68}=+1.362827427\) \(a_{69}=+0.222841809\) \(a_{70}=-0.047325629\)
\(a_{71}=-0.985337275\) \(a_{72}=-0.092412628\) \(a_{73}=-1.165589412\) \(a_{74}=+0.227843052\) \(a_{75}=+1.312208900\)
\(a_{76}=-0.711170467\) \(a_{77}=-0.123374339\) \(a_{78}=-0.007452137\) \(a_{79}=-0.765055166\) \(a_{80}=+1.703426007\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.030536426\) \(a_{83}=+0.694547659\) \(a_{84}=+0.105774402\) \(a_{85}=-2.514762449\)
\(a_{86}=-0.026394132\) \(a_{87}=+0.974629454\) \(a_{88}=-0.183037750\) \(a_{89}=-0.199994601\) \(a_{90}=+0.084418648\)
\(a_{91}=+0.017229754\) \(a_{92}=-0.378409266\) \(a_{93}=+0.394594245\) \(a_{94}=+0.096917253\) \(a_{95}=+1.312289986\)
\(a_{96}=+0.236166262\) \(a_{97}=-0.276570152\) \(a_{98}=-0.135102203\) \(a_{99}=+0.220073036\) \(a_{100}=-2.228271299\)

Showing 100 of 1228 available coefficients

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