Properties

Level $12$
Weight $0$
Character 12.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 12.1825187967 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.307573418\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.154502576\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.186279257\) \(a_{12}=+0.000000000\) \(a_{13}=+0.363821598\) \(a_{14}=+0.000000000\) \(a_{15}=+0.177577596\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.786909572\) \(a_{18}=+0.000000000\) \(a_{19}=+0.756896087\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.089202104\) \(a_{22}=+0.000000000\) \(a_{23}=-1.493392934\) \(a_{24}=+0.000000000\) \(a_{25}=-0.905398592\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.849596250\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.460036474\) \(a_{32}=+0.000000000\) \(a_{33}=+0.107548379\) \(a_{34}=+0.000000000\) \(a_{35}=-0.047520885\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.843088931\) \(a_{38}=+0.000000000\) \(a_{39}=+0.210052497\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.209179152\) \(a_{42}=+0.000000000\) \(a_{43}=+1.201725779\) \(a_{44}=+0.000000000\) \(a_{45}=+0.102524473\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.605654472\) \(a_{48}=+0.000000000\) \(a_{49}=-0.976128954\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.454322453\) \(a_{52}=+0.000000000\) \(a_{53}=-0.428082021\) \(a_{54}=+0.000000000\) \(a_{55}=+0.057294548\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.436994160\) \(a_{58}=+0.000000000\) \(a_{59}=+0.394494495\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.295203030\) \(a_{62}=+0.000000000\) \(a_{63}=-0.051500859\) \(a_{64}=+0.000000000\) \(a_{65}=+0.111901853\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.011272152\) \(a_{68}=+0.000000000\) \(a_{69}=-0.862210812\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.530135482\) \(a_{72}=+0.000000000\) \(a_{73}=+0.097158378\) \(a_{74}=+0.000000000\) \(a_{75}=-0.522732121\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.028780625\) \(a_{78}=+0.000000000\) \(a_{79}=+1.296989354\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.054931474\) \(a_{84}=+0.000000000\) \(a_{85}=+0.242032466\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.490514624\) \(a_{88}=+0.000000000\) \(a_{89}=-0.506706894\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.056211375\) \(a_{92}=+0.000000000\) \(a_{93}=+0.265602182\) \(a_{94}=+0.000000000\) \(a_{95}=+0.232801121\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.510031279\) \(a_{98}=+0.000000000\) \(a_{99}=+0.062093086\) \(a_{100}=+0.000000000\)

Showing 100 of 190 available coefficients

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