Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.15565536137 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.983213057\) \(a_{3}=+0.577350269\) \(a_{4}=-0.033292085\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.567658323\) \(a_{7}=-1.699119683\) \(a_{8}=-1.015946269\) \(a_{9}=+0.333333333\) \(a_{10}=+0.439706246\)
\(a_{11}=-0.390032651\) \(a_{12}=-0.019221194\) \(a_{13}=-0.034005457\) \(a_{14}=-1.670596657\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.965599552\) \(a_{17}=+0.351065403\) \(a_{18}=+0.327737686\) \(a_{19}=-0.796738474\) \(a_{20}=-0.014888673\)
\(a_{21}=-0.980987206\) \(a_{22}=-0.383485195\) \(a_{23}=-1.261777188\) \(a_{24}=-0.586556852\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.033434609\) \(a_{27}=+0.192450090\) \(a_{28}=+0.056567237\) \(a_{29}=-1.743635332\) \(a_{30}=+0.253864520\)
\(a_{31}=+0.351350979\) \(a_{32}=+0.066556182\) \(a_{33}=-0.225185456\) \(a_{34}=+0.345172088\) \(a_{35}=-0.759869423\)
\(a_{36}=-0.011097362\) \(a_{37}=+1.284156749\) \(a_{38}=-0.783363670\) \(a_{39}=-0.019633060\) \(a_{40}=-0.454344984\)
\(a_{41}=+1.017651159\) \(a_{42}=-0.964519430\) \(a_{43}=+0.514576715\) \(a_{44}=+0.012985001\) \(a_{45}=+0.149071199\)
\(a_{46}=-1.240595806\) \(a_{47}=-1.906213176\) \(a_{48}=-0.557489161\) \(a_{49}=+1.887007697\) \(a_{50}=+0.196642611\)
\(a_{51}=+0.202687705\) \(a_{52}=+0.001132113\) \(a_{53}=+1.188606947\) \(a_{54}=+0.189219441\) \(a_{55}=-0.174427905\)
\(a_{56}=+1.726214303\) \(a_{57}=-0.459997172\) \(a_{58}=-1.714365024\) \(a_{59}=+0.850904081\) \(a_{60}=-0.008595980\)
\(a_{61}=-0.858005780\) \(a_{62}=+0.345452868\) \(a_{63}=-0.566373227\) \(a_{64}=+1.031038463\) \(a_{65}=-0.015207696\)
\(a_{66}=-0.221405282\) \(a_{67}=-1.440694274\) \(a_{68}=-0.011687708\) \(a_{69}=-0.728487411\) \(a_{70}=-0.747113526\)
\(a_{71}=-0.379463242\) \(a_{72}=-0.338648720\) \(a_{73}=+1.512033770\) \(a_{74}=+1.262599642\) \(a_{75}=+0.115470054\)
\(a_{76}=+0.026525086\) \(a_{77}=+0.662712154\) \(a_{78}=-0.019303482\) \(a_{79}=-0.445352194\) \(a_{80}=-0.431829245\)
\(a_{81}=+0.111111107\) \(a_{82}=+1.000567903\) \(a_{83}=+0.662377706\) \(a_{84}=+0.032659117\) \(a_{85}=+0.157001217\)
\(a_{86}=+0.505938546\) \(a_{87}=-1.006688321\) \(a_{88}=+0.396252216\) \(a_{89}=-1.239510207\) \(a_{90}=+0.146568735\)
\(a_{91}=+0.057779367\) \(a_{92}=+0.042007209\) \(a_{93}=+0.202852587\) \(a_{94}=-1.874213707\) \(a_{95}=-0.356312266\)
\(a_{96}=+0.038426197\) \(a_{97}=-1.513453287\) \(a_{98}=+1.855330630\) \(a_{99}=-0.130010807\) \(a_{100}=-0.006658416\)

Showing 100 of 1500 available coefficients

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