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: \( 8.28893108415 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.569126088\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.013102538\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.443956186\) \(a_{12}=+0.000000000\) \(a_{13}=+1.227015884\) \(a_{14}=+0.000000000\) \(a_{15}=+0.905935369\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.494553964\) \(a_{18}=+0.000000000\) \(a_{19}=+0.514836115\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.007564754\) \(a_{22}=+0.000000000\) \(a_{23}=+0.040508028\) \(a_{24}=+0.000000000\) \(a_{25}=+1.462156679\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.134955223\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.040816323\) \(a_{32}=+0.000000000\) \(a_{33}=-0.833668493\) \(a_{34}=+0.000000000\) \(a_{35}=+0.020559535\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.724325825\) \(a_{38}=+0.000000000\) \(a_{39}=+0.708417951\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.431377419\) \(a_{42}=+0.000000000\) \(a_{43}=+0.375833390\) \(a_{44}=+0.000000000\) \(a_{45}=+0.523042029\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.889450295\) \(a_{48}=+0.000000000\) \(a_{49}=-0.999828325\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.862881143\) \(a_{52}=+0.000000000\) \(a_{53}=+0.681970678\) \(a_{54}=+0.000000000\) \(a_{55}=-2.265749336\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.297240769\) \(a_{58}=+0.000000000\) \(a_{59}=+0.532960799\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.154592986\) \(a_{62}=+0.000000000\) \(a_{63}=+0.004367513\) \(a_{64}=+0.000000000\) \(a_{65}=+1.925342633\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.245503722\) \(a_{68}=+0.000000000\) \(a_{69}=+0.023387321\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.573135230\) \(a_{72}=+0.000000000\) \(a_{73}=-0.563356418\) \(a_{74}=+0.000000000\) \(a_{75}=+0.844176552\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.018919492\) \(a_{78}=+0.000000000\) \(a_{79}=-1.960295513\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111110\) \(a_{82}=+0.000000000\) \(a_{83}=-1.630618206\) \(a_{84}=+0.000000000\) \(a_{85}=+2.345143612\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.077916434\) \(a_{88}=+0.000000000\) \(a_{89}=+0.968407498\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.016077016\) \(a_{92}=+0.000000000\) \(a_{93}=+0.600915579\) \(a_{94}=+0.000000000\) \(a_{95}=+0.807842762\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.742687283\) \(a_{98}=+0.000000000\) \(a_{99}=-0.481318729\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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