Properties

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

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.68822371255 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.978946011\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.854670890\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.597230732\) \(a_{12}=+0.000000000\) \(a_{13}=-0.118628048\) \(a_{14}=+0.000000000\) \(a_{15}=-0.565194743\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.103585228\) \(a_{18}=+0.000000000\) \(a_{19}=-1.671290918\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.493444468\) \(a_{22}=+0.000000000\) \(a_{23}=-0.285658447\) \(a_{24}=+0.000000000\) \(a_{25}=-0.041664708\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450089\) \(a_{28}=+0.000000000\) \(a_{29}=+0.570689369\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.859829810\) \(a_{32}=+0.000000000\) \(a_{33}=-0.922161599\) \(a_{34}=+0.000000000\) \(a_{35}=-0.836676648\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.741321203\) \(a_{38}=+0.000000000\) \(a_{39}=-0.068489995\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.575980711\) \(a_{42}=+0.000000000\) \(a_{43}=+1.865063314\) \(a_{44}=+0.000000000\) \(a_{45}=-0.326315336\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.864611004\) \(a_{48}=+0.000000000\) \(a_{49}=-0.269537675\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.637155217\) \(a_{52}=+0.000000000\) \(a_{53}=-0.853883171\) \(a_{54}=+0.000000000\) \(a_{55}=+1.563602670\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.964920258\) \(a_{58}=+0.000000000\) \(a_{59}=+1.355902923\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.668366771\) \(a_{62}=+0.000000000\) \(a_{63}=+0.284890303\) \(a_{64}=+0.000000000\) \(a_{65}=+0.116130451\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.514947965\) \(a_{68}=+0.000000000\) \(a_{69}=-0.164925020\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.441230614\) \(a_{72}=+0.000000000\) \(a_{73}=+0.065522110\) \(a_{74}=+0.000000000\) \(a_{75}=-0.024055150\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.365106585\) \(a_{78}=+0.000000000\) \(a_{79}=-0.571762070\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111090\) \(a_{82}=+0.000000000\) \(a_{83}=+1.003238270\) \(a_{84}=+0.000000000\) \(a_{85}=+1.080350323\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.329487677\) \(a_{88}=+0.000000000\) \(a_{89}=-0.155750528\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.101387877\) \(a_{92}=+0.000000000\) \(a_{93}=-0.496423004\) \(a_{94}=+0.000000000\) \(a_{95}=+1.636103567\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.222516431\) \(a_{98}=+0.000000000\) \(a_{99}=-0.532410216\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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