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: \( 4.98315181103 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.852975797\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.184206232\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.459748585\) \(a_{12}=+0.000000000\) \(a_{13}=+1.335999708\) \(a_{14}=+0.000000000\) \(a_{15}=-1.069816075\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.527126289\) \(a_{18}=+0.000000000\) \(a_{19}=+0.490413586\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.106351518\) \(a_{22}=+0.000000000\) \(a_{23}=-0.893684803\) \(a_{24}=+0.000000000\) \(a_{25}=+2.433519302\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.333223343\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.491158756\) \(a_{32}=+0.000000000\) \(a_{33}=-0.265435969\) \(a_{34}=+0.000000000\) \(a_{35}=+0.341329690\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.602711469\) \(a_{38}=+0.000000000\) \(a_{39}=-0.771339791\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.772125886\) \(a_{42}=+0.000000000\) \(a_{43}=+0.797984892\) \(a_{44}=+0.000000000\) \(a_{45}=+0.617658599\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.443783059\) \(a_{48}=+0.000000000\) \(a_{49}=-0.966068064\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.304336505\) \(a_{52}=+0.000000000\) \(a_{53}=-1.206901445\) \(a_{54}=+0.000000000\) \(a_{55}=+0.851903000\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.283140416\) \(a_{58}=+0.000000000\) \(a_{59}=-1.129607097\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.189218675\) \(a_{62}=+0.000000000\) \(a_{63}=+0.061402077\) \(a_{64}=+0.000000000\) \(a_{65}=+2.475575123\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.021029563\) \(a_{68}=+0.000000000\) \(a_{69}=+0.515969162\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.039714350\) \(a_{72}=+0.000000000\) \(a_{73}=-1.197906340\) \(a_{74}=+0.000000000\) \(a_{75}=-1.404993024\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.084688555\) \(a_{78}=+0.000000000\) \(a_{79}=+0.902668170\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.645306200\) \(a_{84}=+0.000000000\) \(a_{85}=-0.976752255\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.192386587\) \(a_{88}=+0.000000000\) \(a_{89}=-0.161891000\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.246099473\) \(a_{92}=+0.000000000\) \(a_{93}=+0.860920909\) \(a_{94}=+0.000000000\) \(a_{95}=+0.908724505\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.979643002\) \(a_{98}=+0.000000000\) \(a_{99}=+0.153249528\) \(a_{100}=+0.000000000\)

Showing 100 of 136 available coefficients

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