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: \( 4.06617926104 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.879586340\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.090879956\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.335249565\) \(a_{12}=+0.000000000\) \(a_{13}=-1.738206096\) \(a_{14}=+0.000000000\) \(a_{15}=+0.507829410\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.768424365\) \(a_{18}=+0.000000000\) \(a_{19}=+0.142314299\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.629819836\) \(a_{22}=+0.000000000\) \(a_{23}=+0.779841856\) \(a_{24}=+0.000000000\) \(a_{25}=-0.226327871\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.122893588\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.109626848\) \(a_{32}=+0.000000000\) \(a_{33}=-0.770906695\) \(a_{34}=+0.000000000\) \(a_{35}=+0.959523108\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.454485484\) \(a_{38}=+0.000000000\) \(a_{39}=+1.003553759\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.338919724\) \(a_{42}=+0.000000000\) \(a_{43}=+0.552278860\) \(a_{44}=+0.000000000\) \(a_{45}=-0.293195447\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.974171881\) \(a_{48}=+0.000000000\) \(a_{49}=+0.190019078\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.443650014\) \(a_{52}=+0.000000000\) \(a_{53}=-0.898790861\) \(a_{54}=+0.000000000\) \(a_{55}=-1.174467277\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.082165199\) \(a_{58}=+0.000000000\) \(a_{59}=+1.047980953\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.166150234\) \(a_{62}=+0.000000000\) \(a_{63}=-0.363626652\) \(a_{64}=+0.000000000\) \(a_{65}=+1.528902335\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.569117616\) \(a_{68}=+0.000000000\) \(a_{69}=-0.450241904\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.076960617\) \(a_{72}=+0.000000000\) \(a_{73}=-0.008669817\) \(a_{74}=+0.000000000\) \(a_{75}=+0.130670305\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.456597157\) \(a_{78}=+0.000000000\) \(a_{79}=-1.305081529\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111110352\) \(a_{82}=+0.000000000\) \(a_{83}=+1.198562310\) \(a_{84}=+0.000000000\) \(a_{85}=+0.675895575\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.070952645\) \(a_{88}=+0.000000000\) \(a_{89}=-1.909772964\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.896174190\) \(a_{92}=+0.000000000\) \(a_{93}=+0.640643354\) \(a_{94}=+0.000000000\) \(a_{95}=-0.125177711\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.221926730\) \(a_{98}=+0.000000000\) \(a_{99}=+0.445083181\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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