Properties

Level $18$
Weight $0$
Character 18.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 12.3124665415 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+1.850220724\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.859822817\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-1.308303621\)
\(a_{11}=+1.901837996\) \(a_{12}=+0.000000000\) \(a_{13}=+0.792036633\) \(a_{14}=+0.607986545\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.986266640\) \(a_{18}=+0.000000000\) \(a_{19}=+0.301498374\) \(a_{20}=+0.925110362\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.344802544\) \(a_{23}=-0.889905481\) \(a_{24}=+0.000000000\) \(a_{25}=+2.423316727\)
\(a_{26}=-0.560054474\) \(a_{27}=+0.000000000\) \(a_{28}=-0.429911409\) \(a_{29}=-0.299609737\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.048464759\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.697395829\) \(a_{35}=-1.590861996\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.763023159\) \(a_{38}=-0.213191545\) \(a_{39}=+0.000000000\) \(a_{40}=-0.654151810\)
\(a_{41}=-0.312911856\) \(a_{42}=+0.000000000\) \(a_{43}=+0.061945380\) \(a_{44}=+0.950918998\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.629258200\) \(a_{47}=+0.477681459\) \(a_{48}=+0.000000000\) \(a_{49}=-0.260704723\) \(a_{50}=-1.713543691\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.396018317\) \(a_{53}=+0.224787298\) \(a_{54}=+0.000000000\) \(a_{55}=+3.518820074\)
\(a_{56}=+0.303993272\) \(a_{57}=+0.000000000\) \(a_{58}=+0.211856077\) \(a_{59}=-0.786394467\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.199765725\) \(a_{62}=+0.034269760\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+1.465442593\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.469154996\) \(a_{68}=+0.493133320\) \(a_{69}=+0.000000000\) \(a_{70}=+1.124909305\)
\(a_{71}=-1.080510366\) \(a_{72}=+0.000000000\) \(a_{73}=+1.060418550\) \(a_{74}=+0.539538850\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.150749187\) \(a_{77}=-1.635243704\) \(a_{78}=+0.000000000\) \(a_{79}=-0.657435234\) \(a_{80}=+0.462555181\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.221262095\) \(a_{83}=-0.579904488\) \(a_{84}=+0.000000000\) \(a_{85}=+1.824810977\)
\(a_{86}=-0.043801998\) \(a_{87}=+0.000000000\) \(a_{88}=-0.672401272\) \(a_{89}=+1.856373231\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.681011170\) \(a_{92}=-0.444952740\) \(a_{93}=+0.000000000\) \(a_{94}=-0.337771799\) \(a_{95}=+0.557838540\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.363189413\) \(a_{98}=+0.184346077\) \(a_{99}=+0.000000000\) \(a_{100}=+1.211658364\)

Showing 100 of 270 available coefficients

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