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: \( 2.74421107125 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.136730716\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.355869689\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.133742799\) \(a_{12}=+0.000000000\) \(a_{13}=+0.672953142\) \(a_{14}=+0.000000000\) \(a_{15}=+0.656291785\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.372452608\) \(a_{18}=+0.000000000\) \(a_{19}=-0.986225324\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.782811730\) \(a_{22}=+0.000000000\) \(a_{23}=+0.726063126\) \(a_{24}=+0.000000000\) \(a_{25}=+0.292156721\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.175525703\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.327703452\) \(a_{32}=+0.000000000\) \(a_{33}=-0.077216441\) \(a_{34}=+0.000000000\) \(a_{35}=-1.541258723\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.599822082\) \(a_{38}=+0.000000000\) \(a_{39}=+0.388529678\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.418037765\) \(a_{42}=+0.000000000\) \(a_{43}=-0.374593185\) \(a_{44}=+0.000000000\) \(a_{45}=+0.378910239\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.911271922\) \(a_{48}=+0.000000000\) \(a_{49}=+0.838382613\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.215035614\) \(a_{52}=+0.000000000\) \(a_{53}=-0.673732595\) \(a_{54}=+0.000000000\) \(a_{55}=-0.152029548\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.569397457\) \(a_{58}=+0.000000000\) \(a_{59}=+0.709609780\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.561700540\) \(a_{62}=+0.000000000\) \(a_{63}=-0.451956563\) \(a_{64}=+0.000000000\) \(a_{65}=+0.764966507\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.358773870\) \(a_{68}=+0.000000000\) \(a_{69}=+0.419192741\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.734241300\) \(a_{72}=+0.000000000\) \(a_{73}=+1.685354700\) \(a_{74}=+0.000000000\) \(a_{75}=+0.168676762\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.181337807\) \(a_{78}=+0.000000000\) \(a_{79}=+0.523356600\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.567837000\) \(a_{84}=+0.000000000\) \(a_{85}=-0.423378320\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.678690081\) \(a_{88}=+0.000000000\) \(a_{89}=-1.111870000\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.912436767\) \(a_{92}=+0.000000000\) \(a_{93}=-0.189199676\) \(a_{94}=+0.000000000\) \(a_{95}=-1.121072619\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.528499603\) \(a_{98}=+0.000000000\) \(a_{99}=-0.044580933\) \(a_{100}=+0.000000000\)

Showing 100 of 126 available coefficients

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