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: \( 5.23156860277 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.061377021\) \(a_{3}=-0.577350269\) \(a_{4}=-0.996232861\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.035436040\) \(a_{7}=+1.885964320\) \(a_{8}=-0.122522826\) \(a_{9}=+0.333333333\) \(a_{10}=+0.027448638\)
\(a_{11}=-0.086511273\) \(a_{12}=+0.575175311\) \(a_{13}=+0.057452342\) \(a_{14}=+0.115754871\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.988712775\) \(a_{17}=+1.244046313\) \(a_{18}=+0.020459007\) \(a_{19}=-0.691597270\) \(a_{20}=-0.445528880\)
\(a_{21}=-1.088862008\) \(a_{22}=-0.005309804\) \(a_{23}=+0.756351174\) \(a_{24}=+0.070738587\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.003526254\) \(a_{27}=-0.192450090\) \(a_{28}=-1.878859630\) \(a_{29}=+1.593610753\) \(a_{30}=-0.015847479\)
\(a_{31}=+0.895922600\) \(a_{32}=+0.183207071\) \(a_{33}=+0.049947307\) \(a_{34}=+0.076355856\) \(a_{35}=+0.843428884\)
\(a_{36}=-0.332077621\) \(a_{37}=-0.746482662\) \(a_{38}=-0.042448180\) \(a_{39}=-0.033170125\) \(a_{40}=-0.054793873\)
\(a_{41}=-0.731178128\) \(a_{42}=-0.066831106\) \(a_{43}=-1.232535164\) \(a_{44}=+0.086185375\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.046422582\) \(a_{47}=+0.521580010\) \(a_{48}=-0.570833587\) \(a_{49}=+2.556861414\) \(a_{50}=+0.012275404\)
\(a_{51}=-0.718250474\) \(a_{52}=-0.057235911\) \(a_{53}=-0.372214237\) \(a_{54}=-0.011812013\) \(a_{55}=-0.038689017\)
\(a_{56}=-0.231073678\) \(a_{57}=+0.399293870\) \(a_{58}=+0.097811081\) \(a_{59}=+1.306760589\) \(a_{60}=+0.257226218\)
\(a_{61}=-0.925551081\) \(a_{62}=+0.054989060\) \(a_{63}=+0.628654774\) \(a_{64}=-0.977468070\) \(a_{65}=+0.025693467\)
\(a_{66}=+0.003065616\) \(a_{67}=-0.405661561\) \(a_{68}=-1.239359819\) \(a_{69}=-0.436679552\) \(a_{70}=+0.051767158\)
\(a_{71}=+0.710485854\) \(a_{72}=-0.040840949\) \(a_{73}=-0.695706409\) \(a_{74}=-0.045816879\) \(a_{75}=-0.115470055\)
\(a_{76}=+0.688991935\) \(a_{77}=-0.163157160\) \(a_{78}=-0.002035891\) \(a_{79}=+0.376264778\) \(a_{80}=+0.442165775\)
\(a_{81}=+0.111111089\) \(a_{82}=-0.044877497\) \(a_{83}=+0.835279709\) \(a_{84}=+1.084760113\) \(a_{85}=+0.556354426\)
\(a_{86}=-0.075649337\) \(a_{87}=-0.920071598\) \(a_{88}=+0.010599606\) \(a_{89}=-0.234749387\) \(a_{90}=+0.009149546\)
\(a_{91}=+0.108353065\) \(a_{92}=-0.753501891\) \(a_{93}=-0.517261153\) \(a_{94}=+0.032013029\) \(a_{95}=-0.309291707\)
\(a_{96}=-0.105774654\) \(a_{97}=+1.235440692\) \(a_{98}=+0.156932531\) \(a_{99}=-0.028837088\) \(a_{100}=-0.199246563\)

Showing 100 of 1500 available coefficients

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